[{"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"link":[{"url":"https://github.com/boyvolcano/PRR","relation":"software"}]},"file":[{"file_size":624647,"checksum":"42917e086f8c7699f3bccf84f74fe000","date_created":"2023-09-20T08:24:47Z","content_type":"application/pdf","file_name":"2023_LNCS_Sun.pdf","date_updated":"2023-09-20T08:24:47Z","relation":"main_file","success":1,"access_level":"open_access","creator":"dernst","file_id":"14348"}],"date_published":"2023-07-17T00:00:00Z","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031377082"]},"language":[{"iso":"eng"}],"conference":{"location":"Paris, France","end_date":"2023-07-22","name":"CAV: Computer Aided Verification","start_date":"2023-07-17"},"publication":"Computer Aided Verification","has_accepted_license":"1","month":"07","oa_version":"Published Version","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"}],"ddc":["000"],"acknowledgement":"We thank Prof. Bican Xia for valuable information on the exponential theory of reals. The work is partially supported by the National Natural Science Foundation of China (NSFC) with Grant No. 62172271, ERC CoG 863818 (ForM-SMArt), the Hong Kong Research Grants Council ECS Project Number 26208122, the HKUST-Kaisa Joint Research Institute Project Grant HKJRI3A-055 and the HKUST Startup Grant R9272.","volume":13966,"date_updated":"2025-07-14T09:09:57Z","year":"2023","citation":{"mla":"Sun, Yican, et al. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” Computer Aided Verification, vol. 13966, Springer Nature, 2023, pp. 16–39, doi:10.1007/978-3-031-37709-9_2.","short":"Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Computer Aided Verification, Springer Nature, 2023, pp. 16–39.","ista":"Sun Y, Fu H, Chatterjee K, Goharshady AK. 2023. Automated tail bound analysis for probabilistic recurrence relations. Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 13966, 16–39.","apa":"Sun, Y., Fu, H., Chatterjee, K., & Goharshady, A. K. (2023). Automated tail bound analysis for probabilistic recurrence relations. In Computer Aided Verification (Vol. 13966, pp. 16–39). Paris, France: Springer Nature. https://doi.org/10.1007/978-3-031-37709-9_2","ama":"Sun Y, Fu H, Chatterjee K, Goharshady AK. Automated tail bound analysis for probabilistic recurrence relations. In: Computer Aided Verification. Vol 13966. Springer Nature; 2023:16-39. doi:10.1007/978-3-031-37709-9_2","ieee":"Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Automated tail bound analysis for probabilistic recurrence relations,” in Computer Aided Verification, Paris, France, 2023, vol. 13966, pp. 16–39.","chicago":"Sun, Yican, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” In Computer Aided Verification, 13966:16–39. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-37709-9_2."},"abstract":[{"lang":"eng","text":"Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit κ, we consider the tail probability Pr[T≥κ], i.e., the probability that the randomized runtime T of the PRR exceeds κ. Our focus is the formal analysis of tail bounds that aims at finding a tight asymptotic upper bound u≥Pr[T≥κ]. To address this problem, the classical and most well-known approach is the cookbook method by Karp (JACM 1994), while other approaches are mostly limited to deriving tail bounds of specific PRRs via involved custom analysis.\r\nIn this work, we propose a novel approach for deriving the common exponentially-decreasing tail bounds for PRRs whose preprocessing time and random passed sizes observe discrete or (piecewise) uniform distribution and whose recursive call is either a single procedure call or a divide-and-conquer. We first establish a theoretical approach via Markov’s inequality, and then instantiate the theoretical approach with a template-based algorithmic approach via a refined treatment of exponentiation. Experimental evaluation shows that our algorithmic approach is capable of deriving tail bounds that are (i) asymptotically tighter than Karp’s method, (ii) match the best-known manually-derived asymptotic tail bound for QuickSelect, and (iii) is only slightly worse (with a loglogn factor) than the manually-proven optimal asymptotic tail bound for QuickSort. Moreover, our algorithmic approach handles all examples (including realistic PRRs such as QuickSort, QuickSelect, DiameterComputation, etc.) in less than 0.1 s, showing that our approach is efficient in practice."}],"doi":"10.1007/978-3-031-37709-9_2","day":"17","file_date_updated":"2023-09-20T08:24:47Z","page":"16-39","quality_controlled":"1","ec_funded":1,"publisher":"Springer Nature","author":[{"last_name":"Sun","first_name":"Yican","full_name":"Sun, Yican"},{"last_name":"Fu","first_name":"Hongfei","full_name":"Fu, Hongfei"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"}],"_id":"14318","scopus_import":"1","title":"Automated tail bound analysis for probabilistic recurrence relations","alternative_title":["LNCS"],"intvolume":" 13966","publication_status":"published","department":[{"_id":"KrCh"}],"article_processing_charge":"Yes (in subscription journal)","date_created":"2023-09-10T22:01:12Z"},{"ddc":["000"],"acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt), the HKUST-Kaisa Joint Research Institute Project Grant HKJRI3A-055, the HKUST Startup Grant R9272 and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","volume":13371,"external_id":{"isi":["000870304500004"]},"isi":1,"year":"2022","citation":{"ama":"Chatterjee K, Goharshady AK, Meggendorfer T, Zikelic D. Sound and complete certificates for auantitative termination analysis of probabilistic programs. In: Proceedings of the 34th International Conference on Computer Aided Verification. Vol 13371. Springer; 2022:55-78. doi:10.1007/978-3-031-13185-1_4","apa":"Chatterjee, K., Goharshady, A. K., Meggendorfer, T., & Zikelic, D. (2022). Sound and complete certificates for auantitative termination analysis of probabilistic programs. In Proceedings of the 34th International Conference on Computer Aided Verification (Vol. 13371, pp. 55–78). Haifa, Israel: Springer. https://doi.org/10.1007/978-3-031-13185-1_4","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Tobias Meggendorfer, and Dorde Zikelic. “Sound and Complete Certificates for Auantitative Termination Analysis of Probabilistic Programs.” In Proceedings of the 34th International Conference on Computer Aided Verification, 13371:55–78. Springer, 2022. https://doi.org/10.1007/978-3-031-13185-1_4.","ieee":"K. Chatterjee, A. K. Goharshady, T. Meggendorfer, and D. Zikelic, “Sound and complete certificates for auantitative termination analysis of probabilistic programs,” in Proceedings of the 34th International Conference on Computer Aided Verification, Haifa, Israel, 2022, vol. 13371, pp. 55–78.","short":"K. Chatterjee, A.K. Goharshady, T. Meggendorfer, D. Zikelic, in:, Proceedings of the 34th International Conference on Computer Aided Verification, Springer, 2022, pp. 55–78.","mla":"Chatterjee, Krishnendu, et al. “Sound and Complete Certificates for Auantitative Termination Analysis of Probabilistic Programs.” Proceedings of the 34th International Conference on Computer Aided Verification, vol. 13371, Springer, 2022, pp. 55–78, doi:10.1007/978-3-031-13185-1_4.","ista":"Chatterjee K, Goharshady AK, Meggendorfer T, Zikelic D. 2022. Sound and complete certificates for auantitative termination analysis of probabilistic programs. Proceedings of the 34th International Conference on Computer Aided Verification. CAV: Computer Aided Verification, LNCS, vol. 13371, 55–78."},"date_updated":"2025-07-14T09:09:58Z","abstract":[{"text":"We consider the quantitative problem of obtaining lower-bounds on the probability of termination of a given non-deterministic probabilistic program. Specifically, given a non-termination threshold p∈[0,1], we aim for certificates proving that the program terminates with probability at least 1−p. The basic idea of our approach is to find a terminating stochastic invariant, i.e. a subset SI of program states such that (i) the probability of the program ever leaving SI is no more than p, and (ii) almost-surely, the program either leaves SI or terminates.\r\n\r\nWhile stochastic invariants are already well-known, we provide the first proof that the idea above is not only sound, but also complete for quantitative termination analysis. We then introduce a novel sound and complete characterization of stochastic invariants that enables template-based approaches for easy synthesis of quantitative termination certificates, especially in affine or polynomial forms. Finally, by combining this idea with the existing martingale-based methods that are relatively complete for qualitative termination analysis, we obtain the first automated, sound, and relatively complete algorithm for quantitative termination analysis. Notably, our completeness guarantees for quantitative termination analysis are as strong as the best-known methods for the qualitative variant.\r\n\r\nOur prototype implementation demonstrates the effectiveness of our approach on various probabilistic programs. We also demonstrate that our algorithm certifies lower bounds on termination probability for probabilistic programs that are beyond the reach of previous methods.","lang":"eng"}],"day":"07","doi":"10.1007/978-3-031-13185-1_4","file_date_updated":"2022-08-29T09:17:01Z","ec_funded":1,"quality_controlled":"1","page":"55-78","publisher":"Springer","author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Amir Kafshdar","last_name":"Goharshady","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","first_name":"Tobias","last_name":"Meggendorfer","orcid":"0000-0002-1712-2165","full_name":"Meggendorfer, Tobias"},{"id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","full_name":"Zikelic, Dorde","orcid":"0000-0002-4681-1699","last_name":"Zikelic","first_name":"Dorde"}],"scopus_import":"1","_id":"12000","intvolume":" 13371","title":"Sound and complete certificates for auantitative termination analysis of probabilistic programs","alternative_title":["LNCS"],"article_processing_charge":"Yes (in subscription journal)","date_created":"2022-08-28T22:02:02Z","department":[{"_id":"KrCh"}],"publication_status":"published","related_material":{"record":[{"status":"public","id":"14539","relation":"dissertation_contains"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"access_level":"open_access","success":1,"relation":"main_file","creator":"alisjak","file_id":"12003","checksum":"24e0f810ec52735a90ade95198bc641d","file_size":505094,"date_created":"2022-08-29T09:17:01Z","content_type":"application/pdf","file_name":"2022_LNCS_Chatterjee.pdf","date_updated":"2022-08-29T09:17:01Z"}],"type":"conference","date_published":"2022-08-07T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"isbn":["9783031131844"],"eissn":["1611-3349"],"issn":["0302-9743"]},"language":[{"iso":"eng"}],"conference":{"start_date":"2022-08-07","name":"CAV: Computer Aided Verification","end_date":"2022-08-10","location":"Haifa, Israel"},"has_accepted_license":"1","publication":"Proceedings of the 34th International Conference on Computer Aided Verification","month":"08","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"oa_version":"Published Version"},{"year":"2022","citation":{"ama":"Ahmadi A, Chatterjee K, Goharshady AK, Meggendorfer T, Safavi Hemami R, Zikelic D. Algorithms and hardness results for computing cores of Markov chains. In: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Vol 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:10.4230/LIPIcs.FSTTCS.2022.29","apa":"Ahmadi, A., Chatterjee, K., Goharshady, A. K., Meggendorfer, T., Safavi Hemami, R., & Zikelic, D. (2022). Algorithms and hardness results for computing cores of Markov chains. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (Vol. 250). Madras, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29","chicago":"Ahmadi, Ali, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Tobias Meggendorfer, Roodabeh Safavi Hemami, and Dorde Zikelic. “Algorithms and Hardness Results for Computing Cores of Markov Chains.” In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Vol. 250. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. https://doi.org/10.4230/LIPIcs.FSTTCS.2022.29.","ieee":"A. Ahmadi, K. Chatterjee, A. K. Goharshady, T. Meggendorfer, R. Safavi Hemami, and D. Zikelic, “Algorithms and hardness results for computing cores of Markov chains,” in 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Madras, India, 2022, vol. 250.","short":"A. Ahmadi, K. Chatterjee, A.K. Goharshady, T. Meggendorfer, R. Safavi Hemami, D. Zikelic, in:, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.","mla":"Ahmadi, Ali, et al. “Algorithms and Hardness Results for Computing Cores of Markov Chains.” 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, vol. 250, 29, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:10.4230/LIPIcs.FSTTCS.2022.29.","ista":"Ahmadi A, Chatterjee K, Goharshady AK, Meggendorfer T, Safavi Hemami R, Zikelic D. 2022. Algorithms and hardness results for computing cores of Markov chains. 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTC: Foundations of Software Technology and Theoretical Computer Science vol. 250, 29."},"date_updated":"2025-07-14T09:09:55Z","day":"14","doi":"10.4230/LIPIcs.FSTTCS.2022.29","abstract":[{"lang":"eng","text":"Given a Markov chain M = (V, v_0, δ), with state space V and a starting state v_0, and a probability threshold ε, an ε-core is a subset C of states that is left with probability at most ε. More formally, C ⊆ V is an ε-core, iff ℙ[reach (V\\C)] ≤ ε. Cores have been applied in a wide variety of verification problems over Markov chains, Markov decision processes, and probabilistic programs, as a means of discarding uninteresting and low-probability parts of a probabilistic system and instead being able to focus on the states that are likely to be encountered in a real-world run. In this work, we focus on the problem of computing a minimal ε-core in a Markov chain. Our contributions include both negative and positive results: (i) We show that the decision problem on the existence of an ε-core of a given size is NP-complete. This solves an open problem posed in [Jan Kretínský and Tobias Meggendorfer, 2020]. We additionally show that the problem remains NP-complete even when limited to acyclic Markov chains with bounded maximal vertex degree; (ii) We provide a polynomial time algorithm for computing a minimal ε-core on Markov chains over control-flow graphs of structured programs. A straightforward combination of our algorithm with standard branch prediction techniques allows one to apply the idea of cores to find a subset of program lines that are left with low probability and then focus any desired static analysis on this core subset."}],"acknowledgement":"The research was partially supported by the Hong Kong Research Grants Council ECS\r\nProject No. 26208122, ERC CoG 863818 (FoRM-SMArt), the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385, HKUST– Kaisa Joint Research Institute Project Grant HKJRI3A-055 and HKUST Startup Grant R9272. Ali Ahmadi and Roodabeh Safavi were interns at HKUST.","volume":250,"ddc":["000"],"scopus_import":"1","_id":"12102","author":[{"first_name":"Ali","last_name":"Ahmadi","full_name":"Ahmadi, Ali"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","last_name":"Goharshady","first_name":"Amir Kafshdar","full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584"},{"full_name":"Meggendorfer, Tobias","orcid":"0000-0002-1712-2165","last_name":"Meggendorfer","first_name":"Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1"},{"full_name":"Safavi Hemami, Roodabeh","first_name":"Roodabeh","last_name":"Safavi Hemami","id":"72ed2640-8972-11ed-ae7b-f9c81ec75154"},{"id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","first_name":"Dorde","last_name":"Zikelic","orcid":"0000-0002-4681-1699","full_name":"Zikelic, Dorde"}],"department":[{"_id":"KrCh"},{"_id":"GradSch"}],"article_processing_charge":"No","date_created":"2023-01-01T23:00:50Z","publication_status":"published","intvolume":" 250","title":"Algorithms and hardness results for computing cores of Markov chains","quality_controlled":"1","ec_funded":1,"file_date_updated":"2023-01-20T10:39:44Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"conference","date_published":"2022-12-14T00:00:00Z","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959772617"]},"oa":1,"file":[{"file_id":"12324","creator":"dernst","relation":"main_file","success":1,"access_level":"open_access","date_updated":"2023-01-20T10:39:44Z","content_type":"application/pdf","file_name":"2022_LIPICs_Ahmadi.pdf","date_created":"2023-01-20T10:39:44Z","checksum":"6660c802489013f034c9e8bd57f4d46e","file_size":872534}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","publication":"42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"name":"International IST Doctoral Program","grant_number":"665385","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","article_number":"29","month":"12","language":[{"iso":"eng"}],"conference":{"start_date":"2022-12-18","name":"FSTTC: Foundations of Software Technology and Theoretical Computer Science","location":"Madras, India","end_date":"2022-12-20"}},{"_id":"8934","author":[{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","first_name":"Amir Kafshdar","last_name":"Goharshady"}],"date_created":"2020-12-10T12:17:07Z","article_processing_charge":"No","department":[{"_id":"KrCh"},{"_id":"GradSch"}],"publication_status":"published","alternative_title":["ISTA Thesis"],"title":"Parameterized and algebro-geometric advances in static program analysis","page":"278","file_date_updated":"2021-12-23T23:30:04Z","publisher":"Institute of Science and Technology Austria","citation":{"short":"A.K. Goharshady, Parameterized and Algebro-Geometric Advances in Static Program Analysis, Institute of Science and Technology Austria, 2021.","mla":"Goharshady, Amir Kafshdar. Parameterized and Algebro-Geometric Advances in Static Program Analysis. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:8934.","ista":"Goharshady AK. 2021. Parameterized and algebro-geometric advances in static program analysis. Institute of Science and Technology Austria.","ama":"Goharshady AK. Parameterized and algebro-geometric advances in static program analysis. 2021. doi:10.15479/AT:ISTA:8934","apa":"Goharshady, A. K. (2021). Parameterized and algebro-geometric advances in static program analysis. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:8934","chicago":"Goharshady, Amir Kafshdar. “Parameterized and Algebro-Geometric Advances in Static Program Analysis.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:8934.","ieee":"A. K. Goharshady, “Parameterized and algebro-geometric advances in static program analysis,” Institute of Science and Technology Austria, 2021."},"year":"2021","date_updated":"2025-06-02T08:53:47Z","day":"01","doi":"10.15479/AT:ISTA:8934","degree_awarded":"PhD","abstract":[{"text":"In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management.\r\nWe use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.","lang":"eng"}],"acknowledgement":"The research was partially supported by an IBM PhD fellowship, a Facebook PhD fellowship, and DOC fellowship #24956 of the Austrian Academy of Sciences (OeAW).","ddc":["005"],"has_accepted_license":"1","project":[{"_id":"267066CE-B435-11E9-9278-68D0E5697425","name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies"},{"_id":"266EEEC0-B435-11E9-9278-68D0E5697425","name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts"}],"oa_version":"Published Version","month":"01","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/publicdomain/zero/1.0/legalcode","short":"CC0 (1.0)","name":"Creative Commons Public Domain Dedication (CC0 1.0)","image":"/images/cc_0.png"},"type":"dissertation","date_published":"2021-01-01T00:00:00Z","publication_identifier":{"issn":["2663-337X"]},"oa":1,"supervisor":[{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"}],"file":[{"date_created":"2020-12-22T20:08:44Z","embargo":"2021-12-22","file_size":5251507,"checksum":"d1b9db3725aed34dadd81274aeb9426c","date_updated":"2021-12-23T23:30:04Z","content_type":"application/pdf","file_name":"Thesis-pdfa.pdf","relation":"main_file","access_level":"open_access","file_id":"8969","creator":"akafshda"},{"file_id":"8970","creator":"akafshda","access_level":"closed","relation":"source_file","date_updated":"2021-03-04T23:30:04Z","file_name":"source.zip","content_type":"application/zip","date_created":"2020-12-22T20:08:50Z","file_size":10636756,"checksum":"1661df7b393e6866d2460eba3c905130","embargo_to":"open_access"}],"status":"public","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"1386"},{"status":"public","id":"1437","relation":"part_of_dissertation"},{"id":"639","relation":"part_of_dissertation","status":"public"},{"id":"6918","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"6490","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"7158"},{"status":"public","id":"6009","relation":"part_of_dissertation"},{"id":"949","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"311","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"7810","status":"public"},{"id":"8089","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"8728","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"5977"},{"relation":"part_of_dissertation","id":"6056","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"6175"},{"id":"6340","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"6378","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"6380","status":"public"},{"id":"66","relation":"part_of_dissertation","status":"public"},{"id":"6780","relation":"part_of_dissertation","status":"public"},{"id":"7014","relation":"part_of_dissertation","status":"public"}]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"type":"conference","date_published":"2021-06-01T00:00:00Z","oa":1,"publication_identifier":{"isbn":["9781450383912"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://hal.archives-ouvertes.fr/hal-03183862/"}],"publication":"Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation","month":"06","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020"},{"name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies","_id":"267066CE-B435-11E9-9278-68D0E5697425"}],"oa_version":"Submitted Version","language":[{"iso":"eng"}],"conference":{"location":"Online","end_date":"2021-06-26","start_date":"2021-06-20","name":" PLDI: Programming Language Design and Implementation"},"external_id":{"isi":["000723661700050"]},"isi":1,"citation":{"ista":"Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. 2021. Polynomial reachability witnesses via Stellensätze. Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. PLDI: Programming Language Design and Implementation, 772–787.","short":"A. Asadi, K. Chatterjee, H. Fu, A.K. Goharshady, M. Mahdavi, in:, Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 772–787.","mla":"Asadi, Ali, et al. “Polynomial Reachability Witnesses via Stellensätze.” Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 772–87, doi:10.1145/3453483.3454076.","ieee":"A. Asadi, K. Chatterjee, H. Fu, A. K. Goharshady, and M. Mahdavi, “Polynomial reachability witnesses via Stellensätze,” in Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Online, 2021, pp. 772–787.","chicago":"Asadi, Ali, Krishnendu Chatterjee, Hongfei Fu, Amir Kafshdar Goharshady, and Mohammad Mahdavi. “Polynomial Reachability Witnesses via Stellensätze.” In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, 772–87. Association for Computing Machinery, 2021. https://doi.org/10.1145/3453483.3454076.","apa":"Asadi, A., Chatterjee, K., Fu, H., Goharshady, A. K., & Mahdavi, M. (2021). Polynomial reachability witnesses via Stellensätze. In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation (pp. 772–787). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454076","ama":"Asadi A, Chatterjee K, Fu H, Goharshady AK, Mahdavi M. Polynomial reachability witnesses via Stellensätze. In: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2021:772-787. doi:10.1145/3453483.3454076"},"year":"2021","date_updated":"2025-07-14T09:10:06Z","abstract":[{"text":"We consider the fundamental problem of reachability analysis over imperative programs with real variables. Previous works that tackle reachability are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic). In contrast, we propose a novel approach for reachability analysis that can handle general and complex loops, is complete, and can be entirely automated for a wide family of programs. Through the notion of Inductive Reachability Witnesses (IRWs), our approach extends ideas from both invariant generation and termination to reachability analysis.\r\n\r\nWe first show that our IRW-based approach is sound and complete for reachability analysis of imperative programs. Then, we focus on linear and polynomial programs and develop automated methods for synthesizing linear and polynomial IRWs. In the linear case, we follow the well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial case, where we present a push-button semi-complete algorithm. We achieve this using a novel combination of classical theorems in real algebraic geometry, such as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally, our experimental results show we can prove complex reachability objectives over various benchmarks that were beyond the reach of previous methods.","lang":"eng"}],"day":"01","doi":"10.1145/3453483.3454076","acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt), the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research Program, the Facebook PhD Fellowship Program, and DOC Fellowship No. 24956 of the Austrian Academy of Sciences (ÖAW).","author":[{"full_name":"Asadi, Ali","last_name":"Asadi","first_name":"Ali"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"full_name":"Fu, Hongfei","first_name":"Hongfei","last_name":"Fu","id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","first_name":"Amir Kafshdar","last_name":"Goharshady","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mohammad","last_name":"Mahdavi","full_name":"Mahdavi, Mohammad"}],"scopus_import":"1","_id":"9645","title":"Polynomial reachability witnesses via Stellensätze","article_processing_charge":"No","department":[{"_id":"KrCh"}],"date_created":"2021-07-11T22:01:17Z","publication_status":"published","quality_controlled":"1","ec_funded":1,"page":"772-787","publisher":"Association for Computing Machinery"},{"oa":1,"publication_identifier":{"isbn":["9781450383912"]},"type":"conference","date_published":"2021-06-01T00:00:00Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2011.14617"}],"month":"06","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies","_id":"267066CE-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication":"Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation","conference":{"start_date":"2021-06-20","name":"PLDI: Programming Language Design and Implementation","location":"Online","end_date":"2021-06-26"},"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability. The main novelty of our approach is that we prove new and dedicated fixed-point theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixed-point functions. To synthesize such fixed-points, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking supermartingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lower-bounds on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds of exponential form in affine programs, and (iii) provably and significantly tighter upper-bounds than the previous approaches. On the practical side, we show our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are remarkably tighter than previous results, in some cases by thousands of orders of magnitude."}],"day":"01","doi":"10.1145/3453483.3454102","arxiv":1,"external_id":{"arxiv":["2011.14617"],"isi":["000723661700076"]},"isi":1,"year":"2021","citation":{"ama":"Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. Quantitative analysis of assertion violations in probabilistic programs. In: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2021:1171-1186. doi:10.1145/3453483.3454102","apa":"Wang, J., Sun, Y., Fu, H., Chatterjee, K., & Goharshady, A. K. (2021). Quantitative analysis of assertion violations in probabilistic programs. In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation (pp. 1171–1186). Online: Association for Computing Machinery. https://doi.org/10.1145/3453483.3454102","ieee":"J. Wang, Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Quantitative analysis of assertion violations in probabilistic programs,” in Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Online, 2021, pp. 1171–1186.","chicago":"Wang, Jinyi, Yican Sun, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” In Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, 1171–86. Association for Computing Machinery, 2021. https://doi.org/10.1145/3453483.3454102.","mla":"Wang, Jinyi, et al. “Quantitative Analysis of Assertion Violations in Probabilistic Programs.” Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 1171–86, doi:10.1145/3453483.3454102.","short":"J. Wang, Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2021, pp. 1171–1186.","ista":"Wang J, Sun Y, Fu H, Chatterjee K, Goharshady AK. 2021. Quantitative analysis of assertion violations in probabilistic programs. Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation. PLDI: Programming Language Design and Implementation, 1171–1186."},"date_updated":"2025-07-14T09:10:06Z","acknowledgement":"We are very thankful to the anonymous reviewers for the helpful and valuable comments. The work was partially supported by the National Natural Science Foundation of China (NSFC) Grant No. 61802254, the Huawei Innovation Research Program, the ERC CoG 863818 (ForM-SMArt), the Facebook PhD Fellowship Program and DOC Fellowship #24956 of the Austrian Academy of Sciences (ÖAW).","title":"Quantitative analysis of assertion violations in probabilistic programs","department":[{"_id":"KrCh"}],"article_processing_charge":"No","date_created":"2021-07-11T22:01:18Z","publication_status":"published","author":[{"full_name":"Wang, Jinyi","first_name":"Jinyi","last_name":"Wang"},{"first_name":"Yican","last_name":"Sun","full_name":"Sun, Yican"},{"full_name":"Fu, Hongfei","first_name":"Hongfei","last_name":"Fu","id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","first_name":"Amir Kafshdar","last_name":"Goharshady"}],"scopus_import":"1","_id":"9646","publisher":"Association for Computing Machinery","ec_funded":1,"quality_controlled":"1","page":"1171-1186"},{"year":"2020","citation":{"ama":"Chatterjee K, Goharshady AK, Ibsen-Jensen R, Pavlogiannis A. Optimal and perfectly parallel algorithms for on-demand data-flow analysis. In: European Symposium on Programming. Vol 12075. Springer Nature; 2020:112-140. doi:10.1007/978-3-030-44914-8_5","apa":"Chatterjee, K., Goharshady, A. K., Ibsen-Jensen, R., & Pavlogiannis, A. (2020). Optimal and perfectly parallel algorithms for on-demand data-flow analysis. In European Symposium on Programming (Vol. 12075, pp. 112–140). Dublin, Ireland: Springer Nature. https://doi.org/10.1007/978-3-030-44914-8_5","ieee":"K. Chatterjee, A. K. Goharshady, R. Ibsen-Jensen, and A. Pavlogiannis, “Optimal and perfectly parallel algorithms for on-demand data-flow analysis,” in European Symposium on Programming, Dublin, Ireland, 2020, vol. 12075, pp. 112–140.","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Optimal and Perfectly Parallel Algorithms for On-Demand Data-Flow Analysis.” In European Symposium on Programming, 12075:112–40. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-44914-8_5.","mla":"Chatterjee, Krishnendu, et al. “Optimal and Perfectly Parallel Algorithms for On-Demand Data-Flow Analysis.” European Symposium on Programming, vol. 12075, Springer Nature, 2020, pp. 112–40, doi:10.1007/978-3-030-44914-8_5.","short":"K. Chatterjee, A.K. Goharshady, R. Ibsen-Jensen, A. Pavlogiannis, in:, European Symposium on Programming, Springer Nature, 2020, pp. 112–140.","ista":"Chatterjee K, Goharshady AK, Ibsen-Jensen R, Pavlogiannis A. 2020. Optimal and perfectly parallel algorithms for on-demand data-flow analysis. European Symposium on Programming. ESOP: Programming Languages and Systems, LNCS, vol. 12075, 112–140."},"date_updated":"2025-06-02T08:53:42Z","external_id":{"isi":["000681656800005"]},"isi":1,"day":"18","doi":"10.1007/978-3-030-44914-8_5","abstract":[{"lang":"eng","text":"Interprocedural data-flow analyses form an expressive and useful paradigm of numerous static analysis applications, such as live variables analysis, alias analysis and null pointers analysis. The most widely-used framework for interprocedural data-flow analysis is IFDS, which encompasses distributive data-flow functions over a finite domain. On-demand data-flow analyses restrict the focus of the analysis on specific program locations and data facts. This setting provides a natural split between (i) an offline (or preprocessing) phase, where the program is partially analyzed and analysis summaries are created, and (ii) an online (or query) phase, where analysis queries arrive on demand and the summaries are used to speed up answering queries.\r\nIn this work, we consider on-demand IFDS analyses where the queries concern program locations of the same procedure (aka same-context queries). We exploit the fact that flow graphs of programs have low treewidth to develop faster algorithms that are space and time optimal for many common data-flow analyses, in both the preprocessing and the query phase. We also use treewidth to develop query solutions that are embarrassingly parallelizable, i.e. the total work for answering each query is split to a number of threads such that each thread performs only a constant amount of work. Finally, we implement a static analyzer based on our algorithms, and perform a series of on-demand analysis experiments on standard benchmarks. Our experimental results show a drastic speed-up of the queries after only a lightweight preprocessing phase, which significantly outperforms existing techniques."}],"volume":12075,"ddc":["000"],"scopus_import":"1","_id":"7810","author":[{"orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","first_name":"Amir Kafshdar","last_name":"Goharshady","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"id":"3B699956-F248-11E8-B48F-1D18A9856A87","last_name":"Ibsen-Jensen","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus","orcid":"0000-0003-4783-0389"},{"orcid":"0000-0002-8943-0722","full_name":"Pavlogiannis, 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4.0)"},"type":"conference","date_published":"2020-04-18T00:00:00Z","publication_identifier":{"isbn":["9783030449131"],"issn":["03029743"],"eissn":["16113349"]},"oa":1,"file":[{"content_type":"application/pdf","file_name":"2020_LNCS_Chatterjee.pdf","date_updated":"2020-07-14T12:48:03Z","file_size":651250,"checksum":"8618b80f4cf7b39a60e61a6445ad9807","date_created":"2020-05-26T13:34:48Z","creator":"dernst","file_id":"7895","access_level":"open_access","relation":"main_file"}],"related_material":{"record":[{"status":"public","id":"8934","relation":"dissertation_contains"}]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","publication":"European Symposium on Programming","project":[{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"grant_number":"ICT15-003","name":"Efficient Algorithms for Computer Aided 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Implementation","conference":{"name":"PLDI: Programming Language Design and Implementation","start_date":"2020-06-15","location":"London, United Kingdom","end_date":"2020-06-20"},"language":[{"iso":"eng"}],"oa":1,"publication_identifier":{"isbn":["9781450376136"]},"type":"conference","date_published":"2020-06-11T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"8934"}]},"main_file_link":[{"url":"https://arxiv.org/abs/1902.04373","open_access":"1"}],"title":"Polynomial invariant generation for non-deterministic recursive programs","department":[{"_id":"KrCh"}],"article_processing_charge":"No","date_created":"2020-07-05T22:00:45Z","publication_status":"published","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87","last_name":"Fu","first_name":"Hongfei","full_name":"Fu, Hongfei"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","first_name":"Amir Kafshdar","last_name":"Goharshady","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar"},{"first_name":"Ehsan Kafshdar","last_name":"Goharshady","full_name":"Goharshady, Ehsan Kafshdar"}],"scopus_import":"1","_id":"8089","publisher":"Association for Computing Machinery","quality_controlled":"1","page":"672-687","abstract":[{"text":"We consider the classical problem of invariant generation for programs with polynomial assignments and focus on synthesizing invariants that are a conjunction of strict polynomial inequalities. We present a sound and semi-complete method based on positivstellensaetze, i.e. theorems in semi-algebraic geometry that characterize positive polynomials over a semi-algebraic set.\r\n\r\nOn the theoretical side, the worst-case complexity of our approach is subexponential, whereas the worst-case complexity of the previous complete method (Kapur, ACA 2004) is doubly-exponential. Even when restricted to linear invariants, the best previous complexity for complete invariant generation is exponential (Colon et al, CAV 2003). On the practical side, we reduce the invariant generation problem to quadratic programming (QCLP), which is a classical optimization problem with many industrial solvers. We demonstrate the applicability of our approach by providing experimental results on several academic benchmarks. To the best of our knowledge, the only previous invariant generation method that provides completeness guarantees for invariants consisting of polynomial inequalities is (Kapur, ACA 2004), which relies on quantifier elimination and cannot even handle toy programs such as our running example.","lang":"eng"}],"day":"11","doi":"10.1145/3385412.3385969","arxiv":1,"external_id":{"arxiv":["1902.04373"],"isi":["000614622300045"]},"isi":1,"year":"2020","citation":{"ieee":"K. Chatterjee, H. Fu, A. K. Goharshady, and E. K. Goharshady, “Polynomial invariant generation for non-deterministic recursive programs,” in Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, London, United Kingdom, 2020, pp. 672–687.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. “Polynomial Invariant Generation for Non-Deterministic Recursive Programs.” In Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, 672–87. Association for Computing Machinery, 2020. https://doi.org/10.1145/3385412.3385969.","apa":"Chatterjee, K., Fu, H., Goharshady, A. K., & Goharshady, E. K. (2020). Polynomial invariant generation for non-deterministic recursive programs. In Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation (pp. 672–687). London, United Kingdom: Association for Computing Machinery. https://doi.org/10.1145/3385412.3385969","ama":"Chatterjee K, Fu H, Goharshady AK, Goharshady EK. Polynomial invariant generation for non-deterministic recursive programs. In: Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2020:672-687. doi:10.1145/3385412.3385969","ista":"Chatterjee K, Fu H, Goharshady AK, Goharshady EK. 2020. Polynomial invariant generation for non-deterministic recursive programs. Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI: Programming Language Design and Implementation, 672–687.","mla":"Chatterjee, Krishnendu, et al. “Polynomial Invariant Generation for Non-Deterministic Recursive Programs.” Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2020, pp. 672–87, doi:10.1145/3385412.3385969.","short":"K. Chatterjee, H. Fu, A.K. Goharshady, E.K. Goharshady, in:, Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2020, pp. 672–687."},"date_updated":"2025-06-02T08:53:42Z"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_id":"8676","creator":"dernst","success":1,"relation":"main_file","access_level":"open_access","date_updated":"2020-10-19T11:14:20Z","content_type":"application/pdf","file_name":"2020_ijmsi_Shakiba_accepted.pdf","date_created":"2020-10-19T11:14:20Z","checksum":"f299661a6d51cda6d255a76be696f48d","file_size":261688}],"type":"journal_article","date_published":"2020-10-01T00:00:00Z","oa":1,"publication_identifier":{"eissn":["2008-9473"],"issn":["1735-4463"]},"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Iranian Journal of Mathematical Sciences and Informatics","month":"10","project":[{"_id":"267066CE-B435-11E9-9278-68D0E5697425","name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies"}],"oa_version":"Submitted Version","ddc":["000"],"acknowledgement":"We are very grateful to the anonymous reviewer for detailed comments and suggestions that significantly improved the presentation of this paper. The research was partially supported by a DOC fellowship of the Austrian Academy of Sciences.","volume":15,"external_id":{"arxiv":["1805.10672"]},"citation":{"short":"A. Shakiba, A.K. Goharshady, M.R. Hooshmandasl, M. Alambardar Meybodi, Iranian Journal of Mathematical Sciences and Informatics 15 (2020) 117–128.","mla":"Shakiba, A., et al. “A Note on Belief Structures and S-Approximation Spaces.” Iranian Journal of Mathematical Sciences and Informatics, vol. 15, no. 2, Iranian Academic Center for Education, Culture and Research, 2020, pp. 117–28, doi:10.29252/ijmsi.15.2.117.","ista":"Shakiba A, Goharshady AK, Hooshmandasl MR, Alambardar Meybodi M. 2020. A note on belief structures and s-approximation spaces. Iranian Journal of Mathematical Sciences and Informatics. 15(2), 117–128.","ama":"Shakiba A, Goharshady AK, Hooshmandasl MR, Alambardar Meybodi M. A note on belief structures and s-approximation spaces. Iranian Journal of Mathematical Sciences and Informatics. 2020;15(2):117-128. doi:10.29252/ijmsi.15.2.117","apa":"Shakiba, A., Goharshady, A. K., Hooshmandasl, M. R., & Alambardar Meybodi, M. (2020). A note on belief structures and s-approximation spaces. Iranian Journal of Mathematical Sciences and Informatics. Iranian Academic Center for Education, Culture and Research. https://doi.org/10.29252/ijmsi.15.2.117","ieee":"A. Shakiba, A. K. Goharshady, M. R. Hooshmandasl, and M. Alambardar Meybodi, “A note on belief structures and s-approximation spaces,” Iranian Journal of Mathematical Sciences and Informatics, vol. 15, no. 2. Iranian Academic Center for Education, Culture and Research, pp. 117–128, 2020.","chicago":"Shakiba, A., Amir Kafshdar Goharshady, M.R. Hooshmandasl, and M. Alambardar Meybodi. “A Note on Belief Structures and S-Approximation Spaces.” Iranian Journal of Mathematical Sciences and Informatics. Iranian Academic Center for Education, Culture and Research, 2020. https://doi.org/10.29252/ijmsi.15.2.117."},"year":"2020","date_updated":"2023-10-16T09:25:00Z","abstract":[{"lang":"eng","text":"We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space. "}],"day":"01","doi":"10.29252/ijmsi.15.2.117","arxiv":1,"file_date_updated":"2020-10-19T11:14:20Z","quality_controlled":"1","page":"117-128","article_type":"original","publisher":"Iranian Academic Center for Education, Culture and Research","issue":"2","author":[{"full_name":"Shakiba, A.","last_name":"Shakiba","first_name":"A."},{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Hooshmandasl","first_name":"M.R.","full_name":"Hooshmandasl, M.R."},{"last_name":"Alambardar Meybodi","first_name":"M.","full_name":"Alambardar Meybodi, M."}],"scopus_import":"1","_id":"8671","intvolume":" 15","title":"A note on belief structures and s-approximation spaces","date_created":"2020-10-18T22:01:36Z","article_processing_charge":"No","department":[{"_id":"KrCh"}],"publication_status":"published"},{"date_created":"2020-11-06T07:30:05Z","department":[{"_id":"KrCh"}],"article_processing_charge":"No","publication_status":"published","intvolume":" 12302","alternative_title":["LNCS"],"title":"Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth","scopus_import":"1","_id":"8728","author":[{"full_name":"Asadi, Ali","last_name":"Asadi","first_name":"Ali"},{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mohammadi, Kiarash","last_name":"Mohammadi","first_name":"Kiarash"},{"id":"49704004-F248-11E8-B48F-1D18A9856A87","full_name":"Pavlogiannis, Andreas","orcid":"0000-0002-8943-0722","last_name":"Pavlogiannis","first_name":"Andreas"}],"publisher":"Springer Nature","quality_controlled":"1","page":"253-270","file_date_updated":"2020-11-06T07:41:03Z","day":"12","doi":"10.1007/978-3-030-59152-6_14","abstract":[{"text":"Discrete-time Markov Chains (MCs) and Markov Decision Processes (MDPs) are two standard formalisms in system analysis. Their main associated quantitative objectives are hitting probabilities, discounted sum, and mean payoff. Although there are many techniques for computing these objectives in general MCs/MDPs, they have not been thoroughly studied in terms of parameterized algorithms, particularly when treewidth is used as the parameter. This is in sharp contrast to qualitative objectives for MCs, MDPs and graph games, for which treewidth-based algorithms yield significant complexity improvements. In this work, we show that treewidth can also be used to obtain faster algorithms for the quantitative problems. For an MC with n states and m transitions, we show that each of the classical quantitative objectives can be computed in O((n+m)⋅t2) time, given a tree decomposition of the MC with width t. Our results also imply a bound of O(κ⋅(n+m)⋅t2) for each objective on MDPs, where κ is the number of strategy-iteration refinements required for the given input and objective. Finally, we make an experimental evaluation of our new algorithms on low-treewidth MCs and MDPs obtained from the DaCapo benchmark suite. Our experiments show that on low-treewidth MCs and MDPs, our algorithms outperform existing well-established methods by one or more orders of magnitude.","lang":"eng"}],"year":"2020","citation":{"ieee":"A. Asadi, K. Chatterjee, A. K. Goharshady, K. Mohammadi, and A. Pavlogiannis, “Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth,” in Automated Technology for Verification and Analysis, Hanoi, Vietnam, 2020, vol. 12302, pp. 253–270.","chicago":"Asadi, Ali, Krishnendu Chatterjee, Amir Kafshdar Goharshady, Kiarash Mohammadi, and Andreas Pavlogiannis. “Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth.” In Automated Technology for Verification and Analysis, 12302:253–70. Springer Nature, 2020. https://doi.org/10.1007/978-3-030-59152-6_14.","ama":"Asadi A, Chatterjee K, Goharshady AK, Mohammadi K, Pavlogiannis A. Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth. In: Automated Technology for Verification and Analysis. Vol 12302. Springer Nature; 2020:253-270. doi:10.1007/978-3-030-59152-6_14","apa":"Asadi, A., Chatterjee, K., Goharshady, A. K., Mohammadi, K., & Pavlogiannis, A. (2020). Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth. In Automated Technology for Verification and Analysis (Vol. 12302, pp. 253–270). Hanoi, Vietnam: Springer Nature. https://doi.org/10.1007/978-3-030-59152-6_14","ista":"Asadi A, Chatterjee K, Goharshady AK, Mohammadi K, Pavlogiannis A. 2020. Faster algorithms for quantitative analysis of MCs and MDPs with small treewidth. Automated Technology for Verification and Analysis. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 12302, 253–270.","mla":"Asadi, Ali, et al. “Faster Algorithms for Quantitative Analysis of MCs and MDPs with Small Treewidth.” Automated Technology for Verification and Analysis, vol. 12302, Springer Nature, 2020, pp. 253–70, doi:10.1007/978-3-030-59152-6_14.","short":"A. Asadi, K. Chatterjee, A.K. Goharshady, K. Mohammadi, A. Pavlogiannis, in:, Automated Technology for Verification and Analysis, Springer Nature, 2020, pp. 253–270."},"date_updated":"2025-06-02T08:53:43Z","external_id":{"isi":["000723555700014"]},"isi":1,"volume":12302,"ddc":["000"],"project":[{"name":"Rigorous Systems Engineering","grant_number":"S 11407_N23","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003","_id":"25892FC0-B435-11E9-9278-68D0E5697425"},{"_id":"267066CE-B435-11E9-9278-68D0E5697425","name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies"}],"oa_version":"Submitted Version","month":"10","has_accepted_license":"1","publication":"Automated Technology for Verification and Analysis","conference":{"name":"ATVA: Automated Technology for Verification and Analysis","start_date":"2020-10-19","location":"Hanoi, Vietnam","end_date":"2020-10-23"},"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"eisbn":["9783030591526"],"isbn":["9783030591519"]},"oa":1,"type":"conference","date_published":"2020-10-12T00:00:00Z","file":[{"file_name":"2020_LNCS_ATVA_Asadi_accepted.pdf","content_type":"application/pdf","date_updated":"2020-11-06T07:41:03Z","file_size":726648,"checksum":"ae83f27e5b189d5abc2e7514f1b7e1b5","date_created":"2020-11-06T07:41:03Z","creator":"dernst","file_id":"8729","relation":"main_file","access_level":"open_access","success":1}],"status":"public","related_material":{"record":[{"id":"8934","relation":"dissertation_contains","status":"public"}]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"language":[{"iso":"eng"}],"month":"01","article_number":"106665","oa_version":"Preprint","project":[{"_id":"266EEEC0-B435-11E9-9278-68D0E5697425","name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts"}],"publication":"Reliability Engineering and System Safety","related_material":{"record":[{"relation":"dissertation_contains","id":"8934","status":"public"}]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/1712.09692","open_access":"1"}],"oa":1,"publication_identifier":{"issn":["09518320"]},"date_published":"2020-01-01T00:00:00Z","type":"journal_article","article_type":"original","publisher":"Elsevier","quality_controlled":"1","title":"An efficient algorithm for computing network reliability in small treewidth","intvolume":" 193","publication_status":"published","date_created":"2019-09-29T22:00:44Z","article_processing_charge":"No","department":[{"_id":"KrCh"}],"author":[{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mohammadi, Fatemeh","last_name":"Mohammadi","first_name":"Fatemeh"}],"_id":"6918","scopus_import":"1","acknowledgement":"We are grateful to the anonymous reviewers for their comments, which significantly improved the present work. The research was partially supported by the EPSRC Early Career Fellowship EP/R023379/1, grant no. SC7-1718-01 of the London Mathematical Society, an IBM PhD Fellowship, and a DOC Fellowship of the Austrian Academy of Sciences (ÖAW).","volume":193,"abstract":[{"text":"We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge of the network is operable with its associated probability and the problem is to determine the probability of having at least one source-to-target path that is entirely composed of operable edges. This problem is known to be NP-hard.\r\n\r\nWe provide a novel scalable algorithm to solve the Network Reliability problem when the treewidth of the underlying network is small. We also show our algorithm’s applicability for real-world transit networks that have small treewidth, including the metro networks of major cities, such as London and Tokyo. Our algorithm leverages tree decompositions to shrink the original graph into much smaller graphs, for which reliability can be efficiently and exactly computed using a brute force method. To the best of our knowledge, this is the first exact algorithm for Network Reliability that can scale to handle real-world instances of the problem.","lang":"eng"}],"doi":"10.1016/j.ress.2019.106665","arxiv":1,"day":"01","isi":1,"external_id":{"isi":["000501641400050"],"arxiv":["1712.09692"]},"date_updated":"2024-03-25T23:30:18Z","citation":{"chicago":"Goharshady, Amir Kafshdar, and Fatemeh Mohammadi. “An Efficient Algorithm for Computing Network Reliability in Small Treewidth.” Reliability Engineering and System Safety. Elsevier, 2020. https://doi.org/10.1016/j.ress.2019.106665.","ieee":"A. K. Goharshady and F. Mohammadi, “An efficient algorithm for computing network reliability in small treewidth,” Reliability Engineering and System Safety, vol. 193. Elsevier, 2020.","apa":"Goharshady, A. K., & Mohammadi, F. (2020). An efficient algorithm for computing network reliability in small treewidth. Reliability Engineering and System Safety. Elsevier. https://doi.org/10.1016/j.ress.2019.106665","ama":"Goharshady AK, Mohammadi F. An efficient algorithm for computing network reliability in small treewidth. Reliability Engineering and System Safety. 2020;193. doi:10.1016/j.ress.2019.106665","ista":"Goharshady AK, Mohammadi F. 2020. An efficient algorithm for computing network reliability in small treewidth. Reliability Engineering and System Safety. 193, 106665.","short":"A.K. Goharshady, F. Mohammadi, Reliability Engineering and System Safety 193 (2020).","mla":"Goharshady, Amir Kafshdar, and Fatemeh Mohammadi. “An Efficient Algorithm for Computing Network Reliability in Small Treewidth.” Reliability Engineering and System Safety, vol. 193, 106665, Elsevier, 2020, doi:10.1016/j.ress.2019.106665."},"year":"2020"},{"conference":{"end_date":"2019-10-25","location":"Athens, Greece","name":"OOPSLA: Object-oriented Programming, Systems, Languages and Applications","start_date":"2019-10-23"},"language":[{"iso":"eng"}],"project":[{"name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003","_id":"25892FC0-B435-11E9-9278-68D0E5697425"},{"name":"Game Theory","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"},{"_id":"267066CE-B435-11E9-9278-68D0E5697425","name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies"},{"name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts","_id":"266EEEC0-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","article_number":"129","month":"10","has_accepted_license":"1","publication":"Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications ","file":[{"date_created":"2019-08-12T15:40:57Z","file_size":1024643,"checksum":"3482d8ace6fb4991eb7810e3b70f1b9f","date_updated":"2020-07-14T12:47:40Z","file_name":"oopsla-2019.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"6807","creator":"akafshda"},{"file_size":538579,"checksum":"4e5a6fb2b59a75222a4e8335a5a60eac","date_created":"2020-05-12T15:15:14Z","file_name":"2019_ACM_Huang.pdf","content_type":"application/pdf","date_updated":"2020-07-14T12:47:40Z","relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"7821"}],"status":"public","related_material":{"record":[{"status":"public","id":"8934","relation":"dissertation_contains"}]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","image":"/images/cc_by_nc.png","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode"},"type":"conference","date_published":"2019-10-01T00:00:00Z","publisher":"ACM","quality_controlled":"1","ec_funded":1,"file_date_updated":"2020-07-14T12:47:40Z","department":[{"_id":"KrCh"}],"date_created":"2019-08-09T09:54:20Z","article_processing_charge":"No","publication_status":"published","intvolume":" 3","title":"Modular verification for almost-sure termination of probabilistic programs","license":"https://creativecommons.org/licenses/by-nc/4.0/","_id":"6780","author":[{"first_name":"Mingzhang","last_name":"Huang","full_name":"Huang, Mingzhang"},{"first_name":"Hongfei","last_name":"Fu","full_name":"Fu, Hongfei"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar"}],"volume":3,"ddc":["000"],"day":"01","doi":"10.1145/3360555","arxiv":1,"abstract":[{"lang":"eng","text":"In this work, we consider the almost-sure termination problem for probabilistic programs that asks whether a\r\ngiven probabilistic program terminates with probability 1. Scalable approaches for program analysis often\r\nrely on modularity as their theoretical basis. In non-probabilistic programs, the classical variant rule (V-rule)\r\nof Floyd-Hoare logic provides the foundation for modular analysis. Extension of this rule to almost-sure\r\ntermination of probabilistic programs is quite tricky, and a probabilistic variant was proposed in [16]. While the\r\nproposed probabilistic variant cautiously addresses the key issue of integrability, we show that the proposed\r\nmodular rule is still not sound for almost-sure termination of probabilistic programs.\r\nBesides establishing unsoundness of the previous rule, our contributions are as follows: First, we present a\r\nsound modular rule for almost-sure termination of probabilistic programs. Our approach is based on a novel\r\nnotion of descent supermartingales. Second, for algorithmic approaches, we consider descent supermartingales\r\nthat are linear and show that they can be synthesized in polynomial time. Finally, we present experimental\r\nresults on a variety of benchmarks and several natural examples that model various types of nested while\r\nloops in probabilistic programs and demonstrate that our approach is able to efficiently prove their almost-sure\r\ntermination property"}],"year":"2019","citation":{"ista":"Huang M, Fu H, Chatterjee K, Goharshady AK. 2019. Modular verification for almost-sure termination of probabilistic programs. Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications . OOPSLA: Object-oriented Programming, Systems, Languages and Applications vol. 3, 129.","mla":"Huang, Mingzhang, et al. “Modular Verification for Almost-Sure Termination of Probabilistic Programs.” Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications , vol. 3, 129, ACM, 2019, doi:10.1145/3360555.","short":"M. Huang, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications , ACM, 2019.","chicago":"Huang, Mingzhang, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Modular Verification for Almost-Sure Termination of Probabilistic Programs.” In Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications , Vol. 3. ACM, 2019. https://doi.org/10.1145/3360555.","ieee":"M. Huang, H. Fu, K. Chatterjee, and A. K. Goharshady, “Modular verification for almost-sure termination of probabilistic programs,” in Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications , Athens, Greece, 2019, vol. 3.","ama":"Huang M, Fu H, Chatterjee K, Goharshady AK. Modular verification for almost-sure termination of probabilistic programs. In: Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications . Vol 3. ACM; 2019. doi:10.1145/3360555","apa":"Huang, M., Fu, H., Chatterjee, K., & Goharshady, A. K. (2019). Modular verification for almost-sure termination of probabilistic programs. In Proceedings of the 34th ACM International Conference on Object-Oriented Programming, Systems, Languages, and Applications (Vol. 3). Athens, Greece: ACM. https://doi.org/10.1145/3360555"},"date_updated":"2025-06-02T08:53:47Z","external_id":{"arxiv":["1901.06087"]}},{"article_number":"20","month":"10","project":[{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","grant_number":"ICT15-003","name":"Efficient Algorithms for Computer Aided Verification"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies","_id":"267066CE-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts","_id":"266EEEC0-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication":"ACM Transactions on Programming Languages and Systems","language":[{"iso":"eng"}],"oa":1,"type":"journal_article","date_published":"2019-10-01T00:00:00Z","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"639"},{"relation":"dissertation_contains","id":"8934","status":"public"}]},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.00317"}],"intvolume":" 41","title":"Non-polynomial worst-case analysis of recursive programs","department":[{"_id":"KrCh"}],"article_processing_charge":"No","date_created":"2019-11-13T08:33:43Z","publication_status":"published","issue":"4","author":[{"last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hongfei","last_name":"Fu","full_name":"Fu, Hongfei"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar"}],"scopus_import":"1","_id":"7014","article_type":"original","publisher":"ACM","ec_funded":1,"quality_controlled":"1","abstract":[{"text":"We study the problem of developing efficient approaches for proving\r\nworst-case bounds of non-deterministic recursive programs. Ranking functions\r\nare sound and complete for proving termination and worst-case bounds of\r\nnonrecursive programs. First, we apply ranking functions to recursion,\r\nresulting in measure functions. We show that measure functions provide a sound\r\nand complete approach to prove worst-case bounds of non-deterministic recursive\r\nprograms. Our second contribution is the synthesis of measure functions in\r\nnonpolynomial forms. We show that non-polynomial measure functions with\r\nlogarithm and exponentiation can be synthesized through abstraction of\r\nlogarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem\r\nusing linear programming. While previous methods obtain worst-case polynomial\r\nbounds, our approach can synthesize bounds of the form $\\mathcal{O}(n\\log n)$\r\nas well as $\\mathcal{O}(n^r)$ where $r$ is not an integer. We present\r\nexperimental results to demonstrate that our approach can obtain efficiently\r\nworst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the\r\ndivide-and-conquer algorithm for the Closest-Pair problem, where we obtain\r\n$\\mathcal{O}(n \\log n)$ worst-case bound, and (ii) Karatsuba's algorithm for\r\npolynomial multiplication and Strassen's algorithm for matrix multiplication,\r\nwhere we obtain $\\mathcal{O}(n^r)$ bound such that $r$ is not an integer and\r\nclose to the best-known bounds for the respective algorithms.","lang":"eng"}],"day":"01","arxiv":1,"doi":"10.1145/3339984","external_id":{"arxiv":["1705.00317"],"isi":["000564108400001"]},"isi":1,"year":"2019","citation":{"apa":"Chatterjee, K., Fu, H., & Goharshady, A. K. (2019). Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. ACM. https://doi.org/10.1145/3339984","ama":"Chatterjee K, Fu H, Goharshady AK. Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. 2019;41(4). doi:10.1145/3339984","ieee":"K. Chatterjee, H. Fu, and A. K. Goharshady, “Non-polynomial worst-case analysis of recursive programs,” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4. ACM, 2019.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” ACM Transactions on Programming Languages and Systems. ACM, 2019. https://doi.org/10.1145/3339984.","short":"K. Chatterjee, H. Fu, A.K. Goharshady, ACM Transactions on Programming Languages and Systems 41 (2019).","mla":"Chatterjee, Krishnendu, et al. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4, 20, ACM, 2019, doi:10.1145/3339984.","ista":"Chatterjee K, Fu H, Goharshady AK. 2019. Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. 41(4), 20."},"date_updated":"2025-06-02T08:53:47Z","volume":41},{"volume":41,"ddc":["000"],"day":"01","doi":"10.1145/3363525","abstract":[{"text":"Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, and so on. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, and so on. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in an important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect we consider is that the control flow graphs for most programs have constant treewidth.\r\n\r\nOur main contributions are simple and implementable algorithms that support multiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing but can answer subsequent queries significantly faster as compared to the current algorithmic solutions for interprocedural dataflow analysis. We have also implemented our algorithms and evaluated their performance for performing on-demand interprocedural dataflow analysis on various domains, such as for live variable analysis and reaching definitions, on a standard benchmark set. Our experimental results align with our theoretical statements and show that after a lightweight preprocessing, on-demand queries are answered much faster than the standard existing algorithmic approaches.\r\n","lang":"eng"}],"citation":{"mla":"Chatterjee, Krishnendu, et al. “Faster Algorithms for Dynamic Algebraic Queries in Basic RSMs with Constant Treewidth.” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4, 23, ACM, 2019, doi:10.1145/3363525.","short":"K. Chatterjee, A.K. Goharshady, P. Goyal, R. Ibsen-Jensen, A. Pavlogiannis, ACM Transactions on Programming Languages and Systems 41 (2019).","ista":"Chatterjee K, Goharshady AK, Goyal P, Ibsen-Jensen R, Pavlogiannis A. 2019. Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. 41(4), 23.","apa":"Chatterjee, K., Goharshady, A. K., Goyal, P., Ibsen-Jensen, R., & Pavlogiannis, A. (2019). Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. ACM. https://doi.org/10.1145/3363525","ama":"Chatterjee K, Goharshady AK, Goyal P, Ibsen-Jensen R, Pavlogiannis A. Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth. ACM Transactions on Programming Languages and Systems. 2019;41(4). doi:10.1145/3363525","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Prateesh Goyal, Rasmus Ibsen-Jensen, and Andreas Pavlogiannis. “Faster Algorithms for Dynamic Algebraic Queries in Basic RSMs with Constant Treewidth.” ACM Transactions on Programming Languages and Systems. ACM, 2019. https://doi.org/10.1145/3363525.","ieee":"K. Chatterjee, A. K. Goharshady, P. Goyal, R. Ibsen-Jensen, and A. Pavlogiannis, “Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth,” ACM Transactions on Programming Languages and Systems, vol. 41, no. 4. ACM, 2019."},"year":"2019","date_updated":"2024-03-25T23:30:19Z","external_id":{"isi":["000564108400004"]},"isi":1,"publisher":"ACM","article_type":"original","quality_controlled":"1","ec_funded":1,"file_date_updated":"2020-10-08T12:58:10Z","date_created":"2019-12-09T08:33:33Z","article_processing_charge":"No","department":[{"_id":"KrCh"}],"publication_status":"published","intvolume":" 41","title":"Faster algorithms for dynamic algebraic queries in basic RSMs with constant treewidth","scopus_import":"1","_id":"7158","issue":"4","author":[{"first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Goyal","first_name":"Prateesh","full_name":"Goyal, Prateesh"},{"last_name":"Ibsen-Jensen","first_name":"Rasmus","full_name":"Ibsen-Jensen, Rasmus","orcid":"0000-0003-4783-0389","id":"3B699956-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pavlogiannis","first_name":"Andreas","full_name":"Pavlogiannis, Andreas","orcid":"0000-0002-8943-0722","id":"49704004-F248-11E8-B48F-1D18A9856A87"}],"file":[{"date_created":"2020-10-08T12:58:10Z","checksum":"291cc86a07bd010d4815e177dac57b70","file_size":667357,"date_updated":"2020-10-08T12:58:10Z","file_name":"2019_ACMTransactions_Chatterjee.pdf","content_type":"application/pdf","success":1,"access_level":"open_access","relation":"main_file","file_id":"8632","creator":"dernst"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"relation":"dissertation_contains","id":"8934","status":"public"}]},"publication_identifier":{"issn":["0164-0925"]},"oa":1,"type":"journal_article","date_published":"2019-11-01T00:00:00Z","language":[{"iso":"eng"}],"project":[{"_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"}],"oa_version":"Submitted Version","article_number":"23","month":"11","has_accepted_license":"1","publication":"ACM Transactions on Programming Languages and Systems"},{"main_file_link":[{"url":"https://arxiv.org/abs/1902.07986","open_access":"1"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"8934"}]},"date_published":"2019-05-01T00:00:00Z","type":"conference","oa":1,"language":[{"iso":"eng"}],"conference":{"name":"IEEE International Conference on Blockchain and Cryptocurrency","start_date":"2019-05-14","end_date":"2019-05-17","location":"Seoul, Korea"},"publication":"IEEE International Conference on Blockchain and Cryptocurrency","oa_version":"Preprint","project":[{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"},{"name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts","_id":"266EEEC0-B435-11E9-9278-68D0E5697425"},{"name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies","_id":"267066CE-B435-11E9-9278-68D0E5697425"}],"month":"05","article_number":"8751326","date_updated":"2024-03-25T23:30:18Z","citation":{"chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Arash Pourdamghani. “Probabilistic Smart Contracts: Secure Randomness on the Blockchain.” In IEEE International Conference on Blockchain and Cryptocurrency. IEEE, 2019. https://doi.org/10.1109/BLOC.2019.8751326.","ieee":"K. Chatterjee, A. K. Goharshady, and A. Pourdamghani, “Probabilistic smart contracts: Secure randomness on the blockchain,” in IEEE International Conference on Blockchain and Cryptocurrency, Seoul, Korea, 2019.","apa":"Chatterjee, K., Goharshady, A. K., & Pourdamghani, A. (2019). Probabilistic smart contracts: Secure randomness on the blockchain. In IEEE International Conference on Blockchain and Cryptocurrency. Seoul, Korea: IEEE. https://doi.org/10.1109/BLOC.2019.8751326","ama":"Chatterjee K, Goharshady AK, Pourdamghani A. Probabilistic smart contracts: Secure randomness on the blockchain. In: IEEE International Conference on Blockchain and Cryptocurrency. IEEE; 2019. doi:10.1109/BLOC.2019.8751326","ista":"Chatterjee K, Goharshady AK, Pourdamghani A. 2019. Probabilistic smart contracts: Secure randomness on the blockchain. IEEE International Conference on Blockchain and Cryptocurrency. IEEE International Conference on Blockchain and Cryptocurrency, 8751326.","short":"K. Chatterjee, A.K. Goharshady, A. Pourdamghani, in:, IEEE International Conference on Blockchain and Cryptocurrency, IEEE, 2019.","mla":"Chatterjee, Krishnendu, et al. “Probabilistic Smart Contracts: Secure Randomness on the Blockchain.” IEEE International Conference on Blockchain and Cryptocurrency, 8751326, IEEE, 2019, doi:10.1109/BLOC.2019.8751326."},"year":"2019","external_id":{"arxiv":["1902.07986"]},"doi":"10.1109/BLOC.2019.8751326","arxiv":1,"day":"01","abstract":[{"text":"In today's programmable blockchains, smart contracts are limited to being deterministic and non-probabilistic. This lack of randomness is a consequential limitation, given that a wide variety of real-world financial contracts, such as casino games and lotteries, depend entirely on randomness. As a result, several ad-hoc random number generation approaches have been developed to be used in smart contracts. These include ideas such as using an oracle or relying on the block hash. However, these approaches are manipulatable, i.e. their output can be tampered with by parties who might not be neutral, such as the owner of the oracle or the miners.We propose a novel game-theoretic approach for generating provably unmanipulatable pseudorandom numbers on the blockchain. Our approach allows smart contracts to access a trustworthy source of randomness that does not rely on potentially compromised miners or oracles, hence enabling the creation of a new generation of smart contracts that are not limited to being non-probabilistic and can be drawn from the much more general class of probabilistic programs.","lang":"eng"}],"quality_controlled":"1","ec_funded":1,"publisher":"IEEE","_id":"6056","scopus_import":1,"author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar"},{"full_name":"Pourdamghani, Arash","last_name":"Pourdamghani","first_name":"Arash"}],"publication_status":"published","date_created":"2019-02-26T09:03:15Z","department":[{"_id":"KrCh"}],"title":"Probabilistic smart contracts: Secure randomness on the blockchain"},{"ddc":["000"],"external_id":{"isi":["000523190300014"],"arxiv":["1902.04659"]},"isi":1,"year":"2019","citation":{"ista":"Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. 2019. Cost analysis of nondeterministic probabilistic programs. PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation. PLDI: Conference on Programming Language Design and Implementation, 204–220.","mla":"Wang, Peixin, et al. “Cost Analysis of Nondeterministic Probabilistic Programs.” PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2019, pp. 204–20, doi:10.1145/3314221.3314581.","short":"P. Wang, H. Fu, A.K. Goharshady, K. Chatterjee, X. Qin, W. Shi, in:, PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Association for Computing Machinery, 2019, pp. 204–220.","chicago":"Wang, Peixin, Hongfei Fu, Amir Kafshdar Goharshady, Krishnendu Chatterjee, Xudong Qin, and Wenjun Shi. “Cost Analysis of Nondeterministic Probabilistic Programs.” In PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, 204–20. Association for Computing Machinery, 2019. https://doi.org/10.1145/3314221.3314581.","ieee":"P. Wang, H. Fu, A. K. Goharshady, K. Chatterjee, X. Qin, and W. Shi, “Cost analysis of nondeterministic probabilistic programs,” in PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation, Phoenix, AZ, United States, 2019, pp. 204–220.","apa":"Wang, P., Fu, H., Goharshady, A. K., Chatterjee, K., Qin, X., & Shi, W. (2019). Cost analysis of nondeterministic probabilistic programs. In PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (pp. 204–220). Phoenix, AZ, United States: Association for Computing Machinery. https://doi.org/10.1145/3314221.3314581","ama":"Wang P, Fu H, Goharshady AK, Chatterjee K, Qin X, Shi W. Cost analysis of nondeterministic probabilistic programs. In: PLDI 2019: Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation. Association for Computing Machinery; 2019:204-220. doi:10.1145/3314221.3314581"},"date_updated":"2025-06-02T08:53:45Z","abstract":[{"text":"We consider the problem of expected cost analysis over nondeterministic probabilistic programs,\r\nwhich aims at automated methods for analyzing the resource-usage of such programs.\r\nPrevious approaches for this problem could only handle nonnegative bounded costs.\r\nHowever, in many scenarios, such as queuing networks or analysis of cryptocurrency protocols,\r\nboth positive and negative costs are necessary and the costs are unbounded as well.\r\n\r\nIn this work, we present a sound and efficient approach to obtain polynomial bounds on the\r\nexpected accumulated cost of nondeterministic probabilistic programs.\r\nOur approach can handle (a) general positive and negative costs with bounded updates in\r\nvariables; and (b) nonnegative costs with general updates to variables.\r\nWe show that several natural examples which could not be\r\nhandled by previous approaches are captured in our framework.\r\n\r\nMoreover, our approach leads to an efficient polynomial-time algorithm, while no\r\nprevious approach for cost analysis of probabilistic programs could guarantee polynomial runtime.\r\nFinally, we show the effectiveness of our approach using experimental results on a variety of programs for which we efficiently synthesize tight resource-usage bounds.","lang":"eng"}],"day":"08","doi":"10.1145/3314221.3314581","arxiv":1,"file_date_updated":"2020-07-14T12:47:20Z","quality_controlled":"1","ec_funded":1,"page":"204-220","publisher":"Association for Computing Machinery","author":[{"first_name":"Peixin","last_name":"Wang","full_name":"Wang, Peixin"},{"id":"3AAD03D6-F248-11E8-B48F-1D18A9856A87","last_name":"Fu","first_name":"Hongfei","full_name":"Fu, Hongfei"},{"orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","first_name":"Amir Kafshdar","last_name":"Goharshady","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Xudong","last_name":"Qin","full_name":"Qin, Xudong"},{"first_name":"Wenjun","last_name":"Shi","full_name":"Shi, Wenjun"}],"scopus_import":"1","_id":"6175","title":"Cost analysis of nondeterministic probabilistic programs","article_processing_charge":"No","department":[{"_id":"KrCh"}],"date_created":"2019-03-25T10:13:25Z","publication_status":"published","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"record":[{"status":"public","id":"5457","relation":"earlier_version"},{"id":"8934","relation":"dissertation_contains","status":"public"}]},"file":[{"date_updated":"2020-07-14T12:47:20Z","content_type":"application/pdf","file_name":"paper.pdf","date_created":"2019-03-25T10:11:22Z","file_size":4051066,"checksum":"703a5e9b8c8587f2a44085ffd9a4db64","file_id":"6176","creator":"akafshda","relation":"main_file","access_level":"open_access"}],"type":"conference","date_published":"2019-06-08T00:00:00Z","oa":1,"keyword":["Program Cost Analysis","Program Termination","Probabilistic Programs","Martingales"],"language":[{"iso":"eng"}],"conference":{"end_date":"2019-06-26","location":"Phoenix, AZ, United States","name":"PLDI: Conference on Programming Language Design and 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Verification","_id":"25892FC0-B435-11E9-9278-68D0E5697425"},{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23"}],"language":[{"iso":"eng"}],"conference":{"end_date":"2019-04-12","location":"Limassol, Cyprus","start_date":"2019-04-08","name":"ACM Symposium on Applied Computing"},"isi":1,"external_id":{"isi":["000474685800049"]},"date_updated":"2025-06-02T08:53:46Z","year":"2019","citation":{"apa":"Chatterjee, K., Goharshady, A. K., & Pourdamghani, A. (2019). Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. In Proceedings of the 34th ACM Symposium on Applied Computing (Vol. Part F147772, pp. 374–381). Limassol, Cyprus: ACM. https://doi.org/10.1145/3297280.3297319","ama":"Chatterjee K, Goharshady AK, Pourdamghani A. Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. In: Proceedings of the 34th ACM Symposium on Applied Computing. Vol Part F147772. ACM; 2019:374-381. doi:10.1145/3297280.3297319","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Arash Pourdamghani. “Hybrid Mining: Exploiting Blockchain’s Computational Power for Distributed Problem Solving.” In Proceedings of the 34th ACM Symposium on Applied Computing, Part F147772:374–81. ACM, 2019. https://doi.org/10.1145/3297280.3297319.","ieee":"K. Chatterjee, A. K. Goharshady, and A. Pourdamghani, “Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving,” in Proceedings of the 34th ACM Symposium on Applied Computing, Limassol, Cyprus, 2019, vol. Part F147772, pp. 374–381.","mla":"Chatterjee, Krishnendu, et al. “Hybrid Mining: Exploiting Blockchain’s Computational Power for Distributed Problem Solving.” Proceedings of the 34th ACM Symposium on Applied Computing, vol. Part F147772, ACM, 2019, pp. 374–81, doi:10.1145/3297280.3297319.","short":"K. Chatterjee, A.K. Goharshady, A. Pourdamghani, in:, Proceedings of the 34th ACM Symposium on Applied Computing, ACM, 2019, pp. 374–381.","ista":"Chatterjee K, Goharshady AK, Pourdamghani A. 2019. Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving. Proceedings of the 34th ACM Symposium on Applied Computing. ACM Symposium on Applied Computing vol. Part F147772, 374–381."},"abstract":[{"text":"In today's cryptocurrencies, Hashcash proof of work is the most commonly-adopted approach to mining. In Hashcash, when a miner decides to add a block to the chain, she has to solve the difficult computational puzzle of inverting a hash function. While Hashcash has been successfully adopted in both Bitcoin and Ethereum, it has attracted significant and harsh criticism due to its massive waste of electricity, its carbon footprint and environmental effects, and the inherent lack of usefulness in inverting a hash function. Various other mining protocols have been suggested, including proof of stake, in which a miner's chance of adding the next block is proportional to her current balance. However, such protocols lead to a higher entry cost for new miners who might not still have any stake in the cryptocurrency, and can in the worst case lead to an oligopoly, where the rich have complete control over mining. In this paper, we propose Hybrid Mining: a new mining protocol that combines solving real-world useful problems with Hashcash. Our protocol allows new miners to join the network by taking part in Hashcash mining without having to own an initial stake. It also allows nodes of the network to submit hard computational problems whose solutions are of interest in the real world, e.g.~protein folding problems. Then, miners can choose to compete in solving these problems, in lieu of Hashcash, for adding a new block. Hence, Hybrid Mining incentivizes miners to solve useful problems, such as hard computational problems arising in biology, in a distributed manner. It also gives researchers in other areas an easy-to-use tool to outsource their hard computations to the blockchain network, which has enormous computational power, by paying a reward to the miner who solves the problem for them. Moreover, our protocol provides strong security guarantees and is at least as resilient to double spending as Bitcoin.","lang":"eng"}],"doi":"10.1145/3297280.3297319","day":"01","ddc":["004"],"volume":"Part F147772","author":[{"full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Amir Kafshdar","last_name":"Goharshady","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pourdamghani","first_name":"Arash","full_name":"Pourdamghani, Arash"}],"_id":"6378","scopus_import":"1","pubrep_id":"1069","title":"Hybrid Mining: Exploiting blockchain’s computational power for distributed problem solving","publication_status":"published","department":[{"_id":"KrCh"}],"article_processing_charge":"No","date_created":"2019-05-06T12:11:36Z","file_date_updated":"2020-07-14T12:47:29Z","page":"374-381","ec_funded":1,"quality_controlled":"1","publisher":"ACM"},{"publisher":"ACM","ec_funded":1,"quality_controlled":"1","file_date_updated":"2020-07-14T12:47:29Z","date_created":"2019-05-06T12:18:17Z","department":[{"_id":"KrCh"}],"publication_status":"published","intvolume":" 3","title":"Efficient parameterized algorithms for data packing","pubrep_id":"1056","_id":"6380","issue":"POPL","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu"},{"first_name":"Amir Kafshdar","last_name":"Goharshady","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Okati, Nastaran","first_name":"Nastaran","last_name":"Okati"},{"orcid":"0000-0002-8943-0722","full_name":"Pavlogiannis, Andreas","first_name":"Andreas","last_name":"Pavlogiannis","id":"49704004-F248-11E8-B48F-1D18A9856A87"}],"volume":3,"ddc":["004"],"day":"01","doi":"10.1145/3290366","abstract":[{"lang":"eng","text":"There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: We show there is a number q* depending on the cache parameters such that (a) if the access hypergraph of order q* has constant treewidth, then there is a linear-time algorithm for Data Packing; (b)the Data Packing problem remains NP-hard even if the access hypergraph of order q*-1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q* of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses. "}],"citation":{"ista":"Chatterjee K, Goharshady AK, Okati N, Pavlogiannis A. 2019. Efficient parameterized algorithms for data packing. Proceedings of the ACM on Programming Languages. 3(POPL), 53.","short":"K. Chatterjee, A.K. Goharshady, N. Okati, A. Pavlogiannis, Proceedings of the ACM on Programming Languages 3 (2019).","mla":"Chatterjee, Krishnendu, et al. “Efficient Parameterized Algorithms for Data Packing.” Proceedings of the ACM on Programming Languages, vol. 3, no. POPL, 53, ACM, 2019, doi:10.1145/3290366.","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, Nastaran Okati, and Andreas Pavlogiannis. “Efficient Parameterized Algorithms for Data Packing.” Proceedings of the ACM on Programming Languages. ACM, 2019. https://doi.org/10.1145/3290366.","ieee":"K. Chatterjee, A. K. Goharshady, N. Okati, and A. Pavlogiannis, “Efficient parameterized algorithms for data packing,” Proceedings of the ACM on Programming Languages, vol. 3, no. POPL. ACM, 2019.","ama":"Chatterjee K, Goharshady AK, Okati N, Pavlogiannis A. Efficient parameterized algorithms for data packing. Proceedings of the ACM on Programming Languages. 2019;3(POPL). doi:10.1145/3290366","apa":"Chatterjee, K., Goharshady, A. K., Okati, N., & Pavlogiannis, A. (2019). Efficient parameterized algorithms for data packing. Proceedings of the ACM on Programming Languages. ACM. https://doi.org/10.1145/3290366"},"year":"2019","date_updated":"2024-03-25T23:30:18Z","language":[{"iso":"eng"}],"project":[{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003"},{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23"},{"_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications"}],"oa_version":"Published Version","article_number":"53","month":"01","has_accepted_license":"1","publication":"Proceedings of the ACM on Programming Languages","file":[{"file_id":"6381","creator":"dernst","access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:47:29Z","file_name":"2019_ACM_POPL_Chatterjee.pdf","content_type":"application/pdf","date_created":"2019-05-06T12:23:11Z","file_size":1294962,"checksum":"c157752f96877b36685ad7063ada4524"}],"related_material":{"record":[{"status":"public","id":"8934","relation":"dissertation_contains"}]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["2475-1421"]},"oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","date_published":"2019-01-01T00:00:00Z"},{"related_material":{"record":[{"id":"8934","relation":"dissertation_contains","status":"public"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"date_updated":"2020-07-14T12:47:32Z","file_name":"2019_ACM_Chatterjee.pdf","content_type":"application/pdf","date_created":"2020-05-14T09:50:11Z","file_size":6937138,"checksum":"dddc20f6d9881f23b8755eb720ec9d6f","file_id":"7827","creator":"dernst","relation":"main_file","access_level":"open_access"}],"oa":1,"publication_identifier":{"isbn":["9781450359337"]},"type":"conference","date_published":"2019-04-01T00:00:00Z","conference":{"name":"SAC: Symposium on Applied Computing","start_date":"2019-04-08","location":"Limassol, Cyprus","end_date":"2019-04-12"},"language":[{"iso":"eng"}],"month":"04","oa_version":"Submitted Version","has_accepted_license":"1","publication":"Proceedings of the 34th ACM Symposium on Applied Computing","ddc":["000"],"volume":"Part F147772","abstract":[{"lang":"eng","text":"Smart contracts are programs that are stored and executed on the Blockchain and can receive, manage and transfer money (cryptocurrency units). Two important problems regarding smart contracts are formal analysis and compiler optimization. Formal analysis is extremely important, because smart contracts hold funds worth billions of dollars and their code is immutable after deployment. Hence, an undetected bug can cause significant financial losses. Compiler optimization is also crucial, because every action of a smart contract has to be executed by every node in the Blockchain network. Therefore, optimizations in compiling smart contracts can lead to significant savings in computation, time and energy.\r\n\r\nTwo classical approaches in program analysis and compiler optimization are intraprocedural and interprocedural analysis. In intraprocedural analysis, each function is analyzed separately, while interprocedural analysis considers the entire program. In both cases, the analyses are usually reduced to graph problems over the control flow graph (CFG) of the program. These graph problems are often computationally expensive. Hence, there has been ample research on exploiting structural properties of CFGs for efficient algorithms. One such well-studied property is the treewidth, which is a measure of tree-likeness of graphs. It is known that intraprocedural CFGs of structured programs have treewidth at most 6, whereas the interprocedural treewidth cannot be bounded. This result has been used as a basis for many efficient intraprocedural analyses.\r\n\r\nIn this paper, we explore the idea of exploiting the treewidth of smart contracts for formal analysis and compiler optimization. First, similar to classical programs, we show that the intraprocedural treewidth of structured Solidity and Vyper smart contracts is at most 9. Second, for global analysis, we prove that the interprocedural treewidth of structured smart contracts is bounded by 10 and, in sharp contrast with classical programs, treewidth-based algorithms can be easily applied for interprocedural analysis. Finally, we supplement our theoretical results with experiments using a tool we implemented for computing treewidth of smart contracts and show that the treewidth is much lower in practice. We use 36,764 real-world Ethereum smart contracts as benchmarks and find that they have an average treewidth of at most 3.35 for the intraprocedural case and 3.65 for the interprocedural case.\r\n"}],"day":"01","doi":"10.1145/3297280.3297322","external_id":{"isi":["000474685800052"]},"isi":1,"citation":{"short":"K. Chatterjee, A.K. Goharshady, E.K. Goharshady, in:, Proceedings of the 34th ACM Symposium on Applied Computing, ACM, n.d., pp. 400–408.","mla":"Chatterjee, Krishnendu, et al. “The Treewidth of Smart Contracts.” Proceedings of the 34th ACM Symposium on Applied Computing, vol. Part F147772, ACM, pp. 400–08, doi:10.1145/3297280.3297322.","ista":"Chatterjee K, Goharshady AK, Goharshady EK. The treewidth of smart contracts. Proceedings of the 34th ACM Symposium on Applied Computing. SAC: Symposium on Applied Computing vol. Part F147772, 400–408.","ama":"Chatterjee K, Goharshady AK, Goharshady EK. The treewidth of smart contracts. In: Proceedings of the 34th ACM Symposium on Applied Computing. Vol Part F147772. ACM; :400-408. doi:10.1145/3297280.3297322","apa":"Chatterjee, K., Goharshady, A. K., & Goharshady, E. K. (n.d.). The treewidth of smart contracts. In Proceedings of the 34th ACM Symposium on Applied Computing (Vol. Part F147772, pp. 400–408). Limassol, Cyprus: ACM. https://doi.org/10.1145/3297280.3297322","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Ehsan Kafshdar Goharshady. “The Treewidth of Smart Contracts.” In Proceedings of the 34th ACM Symposium on Applied Computing, Part F147772:400–408. ACM, n.d. https://doi.org/10.1145/3297280.3297322.","ieee":"K. Chatterjee, A. K. Goharshady, and E. K. Goharshady, “The treewidth of smart contracts,” in Proceedings of the 34th ACM Symposium on Applied Computing, Limassol, Cyprus, vol. Part F147772, pp. 400–408."},"year":"2019","date_updated":"2024-03-25T23:30:18Z","publisher":"ACM","file_date_updated":"2020-07-14T12:47:32Z","quality_controlled":"1","page":"400-408","pubrep_id":"1070","title":"The treewidth of smart contracts","date_created":"2019-05-26T21:59:15Z","article_processing_charge":"No","department":[{"_id":"KrCh"}],"publication_status":"submitted","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584","last_name":"Goharshady","first_name":"Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ehsan Kafshdar","last_name":"Goharshady","full_name":"Goharshady, Ehsan Kafshdar"}],"scopus_import":"1","_id":"6490"},{"publisher":"Springer","file_date_updated":"2020-07-14T12:46:00Z","quality_controlled":"1","ec_funded":1,"page":"739 - 767","intvolume":" 10801","title":"Quantitative analysis of smart contracts","alternative_title":["LNCS"],"date_created":"2018-12-11T11:45:45Z","department":[{"_id":"KrCh"}],"article_processing_charge":"No","publication_status":"published","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"first_name":"Amir","last_name":"Goharshady","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir","id":"391365CE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Velner","first_name":"Yaron","full_name":"Velner, Yaron"}],"scopus_import":"1","_id":"311","ddc":["000"],"acknowledgement":"The research was partially supported by Vienna Science and Technology Fund (WWTF) Project ICT15-003, Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE), and ERC Starting grant (279307: Graph Games).","volume":10801,"abstract":[{"lang":"eng","text":"Smart contracts are computer programs that are executed by a network of mutually distrusting agents, without the need of an external trusted authority. Smart contracts handle and transfer assets of considerable value (in the form of crypto-currency like Bitcoin). Hence, it is crucial that their implementation is bug-free. We identify the utility (or expected payoff) of interacting with such smart contracts as the basic and canonical quantitative property for such contracts. We present a framework for such quantitative analysis of smart contracts. Such a formal framework poses new and novel research challenges in programming languages, as it requires modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior and modeling utilities which are not specified as standard temporal properties such as safety and termination. While game-theoretic incentives have been analyzed in the security community, their analysis has been restricted to the very special case of stateless games. However, to analyze smart contracts, stateful analysis is required as it must account for the different program states of the protocol. Our main contributions are as follows: we present (i)~a simplified programming language for smart contracts; (ii)~an automatic translation of the programs to state-based games; (iii)~an abstraction-refinement approach to solve such games; and (iv)~experimental results on real-world-inspired smart contracts."}],"day":"01","doi":"10.1007/978-3-319-89884-1_26","citation":{"apa":"Chatterjee, K., Goharshady, A. K., & Velner, Y. (2018). Quantitative analysis of smart contracts (Vol. 10801, pp. 739–767). Presented at the ESOP: European Symposium on Programming, Thessaloniki, Greece: Springer. https://doi.org/10.1007/978-3-319-89884-1_26","ama":"Chatterjee K, Goharshady AK, Velner Y. Quantitative analysis of smart contracts. In: Vol 10801. Springer; 2018:739-767. doi:10.1007/978-3-319-89884-1_26","chicago":"Chatterjee, Krishnendu, Amir Kafshdar Goharshady, and Yaron Velner. “Quantitative Analysis of Smart Contracts,” 10801:739–67. Springer, 2018. https://doi.org/10.1007/978-3-319-89884-1_26.","ieee":"K. Chatterjee, A. K. Goharshady, and Y. Velner, “Quantitative analysis of smart contracts,” presented at the ESOP: European Symposium on Programming, Thessaloniki, Greece, 2018, vol. 10801, pp. 739–767.","mla":"Chatterjee, Krishnendu, et al. Quantitative Analysis of Smart Contracts. Vol. 10801, Springer, 2018, pp. 739–67, doi:10.1007/978-3-319-89884-1_26.","short":"K. Chatterjee, A.K. Goharshady, Y. Velner, in:, Springer, 2018, pp. 739–767.","ista":"Chatterjee K, Goharshady AK, Velner Y. 2018. Quantitative analysis of smart contracts. ESOP: European Symposium on Programming, LNCS, vol. 10801, 739–767."},"year":"2018","date_updated":"2025-06-02T08:53:41Z","conference":{"name":"ESOP: European Symposium on Programming","start_date":"2018-04-16","location":"Thessaloniki, Greece","end_date":"2018-04-19"},"language":[{"iso":"eng"}],"month":"04","project":[{"_id":"25892FC0-B435-11E9-9278-68D0E5697425","name":"Efficient Algorithms for Computer Aided Verification","grant_number":"ICT15-003"},{"call_identifier":"FWF","_id":"25832EC2-B435-11E9-9278-68D0E5697425","name":"Rigorous Systems Engineering","grant_number":"S 11407_N23"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"oa_version":"Published Version","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"relation":"dissertation_contains","id":"8934","status":"public"}]},"status":"public","file":[{"access_level":"open_access","relation":"main_file","creator":"dernst","file_id":"5716","file_size":1394993,"checksum":"9c8a8338c571903b599b6ca93abd2cce","date_created":"2018-12-17T15:45:49Z","content_type":"application/pdf","file_name":"2018_ESOP_Chatterjee.pdf","date_updated":"2020-07-14T12:46:00Z"}],"publist_id":"7554","oa":1,"type":"conference","date_published":"2018-04-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}}]