[{"publication":"Computer Aided Verification","language":[{"iso":"eng"}],"scopus_import":"1","has_accepted_license":"1","intvolume":"     13966","title":"Automated tail bound analysis for probabilistic recurrence relations","oa":1,"date_updated":"2025-07-14T09:09:57Z","article_processing_charge":"Yes (in subscription journal)","alternative_title":["LNCS"],"type":"conference","status":"public","day":"17","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"access_level":"open_access","content_type":"application/pdf","file_size":624647,"relation":"main_file","creator":"dernst","date_created":"2023-09-20T08:24:47Z","date_updated":"2023-09-20T08:24:47Z","success":1,"file_name":"2023_LNCS_Sun.pdf","checksum":"42917e086f8c7699f3bccf84f74fe000","file_id":"14348"}],"conference":{"start_date":"2023-07-17","name":"CAV: Computer Aided Verification","end_date":"2023-07-22","location":"Paris, France"},"publication_identifier":{"issn":["0302-9743"],"isbn":["9783031377082"],"eissn":["1611-3349"]},"month":"07","author":[{"last_name":"Sun","full_name":"Sun, Yican","first_name":"Yican"},{"last_name":"Fu","full_name":"Fu, Hongfei","first_name":"Hongfei"},{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Amir Kafshdar","full_name":"Goharshady, Amir Kafshdar","id":"391365CE-F248-11E8-B48F-1D18A9856A87","last_name":"Goharshady","orcid":"0000-0003-1702-6584"}],"doi":"10.1007/978-3-031-37709-9_2","file_date_updated":"2023-09-20T08:24:47Z","_id":"14318","ec_funded":1,"related_material":{"link":[{"url":"https://github.com/boyvolcano/PRR","relation":"software"}]},"citation":{"short":"Y. Sun, H. Fu, K. Chatterjee, A.K. Goharshady, in:, Computer Aided Verification, Springer Nature, 2023, pp. 16–39.","ieee":"Y. Sun, H. Fu, K. Chatterjee, and A. K. Goharshady, “Automated tail bound analysis for probabilistic recurrence relations,” in <i>Computer Aided Verification</i>, Paris, France, 2023, vol. 13966, pp. 16–39.","ama":"Sun Y, Fu H, Chatterjee K, Goharshady AK. Automated tail bound analysis for probabilistic recurrence relations. In: <i>Computer Aided Verification</i>. Vol 13966. Springer Nature; 2023:16-39. doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">10.1007/978-3-031-37709-9_2</a>","mla":"Sun, Yican, et al. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” <i>Computer Aided Verification</i>, vol. 13966, Springer Nature, 2023, pp. 16–39, doi:<a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">10.1007/978-3-031-37709-9_2</a>.","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.","chicago":"Sun, Yican, Hongfei Fu, Krishnendu Chatterjee, and Amir Kafshdar Goharshady. “Automated Tail Bound Analysis for Probabilistic Recurrence Relations.” In <i>Computer Aided Verification</i>, 13966:16–39. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">https://doi.org/10.1007/978-3-031-37709-9_2</a>.","apa":"Sun, Y., Fu, H., Chatterjee, K., &#38; Goharshady, A. K. (2023). Automated tail bound analysis for probabilistic recurrence relations. In <i>Computer Aided Verification</i> (Vol. 13966, pp. 16–39). Paris, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-37709-9_2\">https://doi.org/10.1007/978-3-031-37709-9_2</a>"},"date_created":"2023-09-10T22:01:12Z","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.","year":"2023","page":"16-39","department":[{"_id":"KrCh"}],"volume":13966,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-07-17T00:00:00Z","project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"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."}],"ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published"},{"department":[{"_id":"KrCh"}],"quality_controlled":"1","volume":272,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_published":"2023-08-21T00:00:00Z","project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"}],"external_id":{"arxiv":["2307.06611"]},"abstract":[{"text":"Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. In the most general case, the problem is decidable subject to Shanuel’s conjecture. If all inputs are rational, the resulting threshold problem can be solved using algebraic numbers, leading to decidability via a polynomial-time reduction to the existential theory of the reals. Further restrictions on the encoding of the input allow the solution of the threshold problem in NP∩coNP. Finally, an approximation algorithm for the optimal value of ERisk is provided.","lang":"eng"}],"ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","doi":"10.4230/LIPIcs.MFCS.2023.15","file_date_updated":"2023-10-09T09:19:11Z","_id":"14417","ec_funded":1,"article_number":"15","citation":{"short":"C. Baier, K. Chatterjee, T. Meggendorfer, J. Piribauer, in:, 48th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023.","ieee":"C. Baier, K. Chatterjee, T. Meggendorfer, and J. Piribauer, “Entropic risk for turn-based stochastic games,” in <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, Bordeaux, France, 2023, vol. 272.","ama":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. Entropic risk for turn-based stochastic games. In: <i>48th International Symposium on Mathematical Foundations of Computer Science</i>. Vol 272. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2023. doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">10.4230/LIPIcs.MFCS.2023.15</a>","mla":"Baier, Christel, et al. “Entropic Risk for Turn-Based Stochastic Games.” <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, vol. 272, 15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023, doi:<a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">10.4230/LIPIcs.MFCS.2023.15</a>.","ista":"Baier C, Chatterjee K, Meggendorfer T, Piribauer J. 2023. Entropic risk for turn-based stochastic games. 48th International Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of Computer Science, LIPIcs, vol. 272, 15.","chicago":"Baier, Christel, Krishnendu Chatterjee, Tobias Meggendorfer, and Jakob Piribauer. “Entropic Risk for Turn-Based Stochastic Games.” In <i>48th International Symposium on Mathematical Foundations of Computer Science</i>, Vol. 272. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">https://doi.org/10.4230/LIPIcs.MFCS.2023.15</a>.","apa":"Baier, C., Chatterjee, K., Meggendorfer, T., &#38; Piribauer, J. (2023). Entropic risk for turn-based stochastic games. In <i>48th International Symposium on Mathematical Foundations of Computer Science</i> (Vol. 272). Bordeaux, France: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.MFCS.2023.15\">https://doi.org/10.4230/LIPIcs.MFCS.2023.15</a>"},"date_created":"2023-10-09T09:21:05Z","acknowledgement":"This work was partly funded by the ERC CoG 863818 (ForM-SMArt), the DFG Grant\r\n389792660 as part of TRR 248 (Foundations of Perspicuous Software Systems), the Cluster of\r\nExcellence EXC 2050/1 (CeTI, project ID 390696704, as part of Germany’s Excellence Strategy), and the DFG projects BA-1679/11-1 and BA-1679/12-1.","year":"2023","alternative_title":["LIPIcs"],"type":"conference","status":"public","oa_version":"Published Version","day":"21","file":[{"checksum":"402281b17ed669bbf149d0fdf68ac201","file_id":"14418","file_name":"2023_LIPIcsMFCS_Baier.pdf","success":1,"date_updated":"2023-10-09T09:19:11Z","date_created":"2023-10-09T09:19:11Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":826843}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"end_date":"2023-09-01","location":"Bordeaux, France","start_date":"2023-08-28","name":"MFCS: Symposium on Mathematical Foundations of Computer Science"},"month":"08","publication_identifier":{"isbn":["9783959772921"],"eissn":["1868-8969"]},"author":[{"full_name":"Baier, Christel","first_name":"Christel","last_name":"Baier"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"orcid":"0000-0002-1712-2165","last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","full_name":"Meggendorfer, Tobias","first_name":"Tobias"},{"full_name":"Piribauer, Jakob","first_name":"Jakob","last_name":"Piribauer"}],"arxiv":1,"publication":"48th International Symposium on Mathematical Foundations of Computer Science","language":[{"iso":"eng"}],"has_accepted_license":"1","scopus_import":"1","intvolume":"       272","title":"Entropic risk for turn-based stochastic games","oa":1,"date_updated":"2025-07-14T09:09:57Z","article_processing_charge":"Yes"},{"related_material":{"link":[{"url":"https://doi.org/10.1007/978-3-031-43587-4_31","relation":"erratum"}]},"date_created":"2023-10-29T23:01:16Z","citation":{"apa":"Křišťan, J. M., &#38; Svoboda, J. (2023). Shortest dominating set reconfiguration under token sliding. In <i>24th International Symposium on Fundamentals of Computation Theory</i> (Vol. 14292, pp. 333–347). Trier, Germany: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-43587-4_24\">https://doi.org/10.1007/978-3-031-43587-4_24</a>","ista":"Křišťan JM, Svoboda J. 2023. Shortest dominating set reconfiguration under token sliding. 24th International Symposium on Fundamentals of Computation Theory. FCT: Fundamentals of Computation Theory, LNCS, vol. 14292, 333–347.","chicago":"Křišťan, Jan Matyáš, and Jakub Svoboda. “Shortest Dominating Set Reconfiguration under Token Sliding.” In <i>24th International Symposium on Fundamentals of Computation Theory</i>, 14292:333–47. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-43587-4_24\">https://doi.org/10.1007/978-3-031-43587-4_24</a>.","mla":"Křišťan, Jan Matyáš, and Jakub Svoboda. “Shortest Dominating Set Reconfiguration under Token Sliding.” <i>24th International Symposium on Fundamentals of Computation Theory</i>, vol. 14292, Springer Nature, 2023, pp. 333–47, doi:<a href=\"https://doi.org/10.1007/978-3-031-43587-4_24\">10.1007/978-3-031-43587-4_24</a>.","short":"J.M. Křišťan, J. Svoboda, in:, 24th International Symposium on Fundamentals of Computation Theory, Springer Nature, 2023, pp. 333–347.","ieee":"J. M. Křišťan and J. Svoboda, “Shortest dominating set reconfiguration under token sliding,” in <i>24th International Symposium on Fundamentals of Computation Theory</i>, Trier, Germany, 2023, vol. 14292, pp. 333–347.","ama":"Křišťan JM, Svoboda J. Shortest dominating set reconfiguration under token sliding. In: <i>24th International Symposium on Fundamentals of Computation Theory</i>. Vol 14292. Springer Nature; 2023:333-347. doi:<a href=\"https://doi.org/10.1007/978-3-031-43587-4_24\">10.1007/978-3-031-43587-4_24</a>"},"year":"2023","doi":"10.1007/978-3-031-43587-4_24","_id":"14456","external_id":{"arxiv":["2307.10847"]},"abstract":[{"text":"In this paper, we present novel algorithms that efficiently compute a shortest reconfiguration sequence between two given dominating sets in trees and interval graphs under the TOKEN SLIDING model. In this problem, a graph is provided along with its two dominating sets, which can be imagined as tokens placed on vertices. The objective is to find a shortest sequence of dominating sets that transforms one set into the other, with each set in the sequence resulting from sliding a single token in the previous set. While identifying any sequence has been well studied, our work presents the first polynomial algorithms for this optimization variant in the context of dominating sets.","lang":"eng"}],"publication_status":"published","page":"333-347","department":[{"_id":"KrCh"}],"quality_controlled":"1","volume":14292,"publisher":"Springer Nature","date_published":"2023-09-21T00:00:00Z","intvolume":"     14292","scopus_import":"1","title":"Shortest dominating set reconfiguration under token sliding","date_updated":"2024-01-22T08:10:49Z","oa":1,"article_processing_charge":"No","publication":"24th International Symposium on Fundamentals of Computation Theory","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.10847","open_access":"1"}],"day":"21","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"location":"Trier, Germany","end_date":"2023-09-21","name":"FCT: Fundamentals of Computation Theory","start_date":"2023-09-18"},"month":"09","publication_identifier":{"issn":["0302-9743"],"eissn":["1611-3349"],"isbn":["9783031435867"]},"author":[{"full_name":"Křišťan, Jan Matyáš","first_name":"Jan Matyáš","last_name":"Křišťan"},{"orcid":"0000-0002-1419-3267","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","full_name":"Svoboda, Jakub","first_name":"Jakub"}],"arxiv":1,"alternative_title":["LNCS"],"status":"public","type":"conference"},{"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"},{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}],"date_published":"2023-09-28T00:00:00Z","publisher":"IOS Press","quality_controlled":"1","volume":372,"department":[{"_id":"ToHe"},{"_id":"KrCh"}],"page":"141-148","publication_status":"published","tmp":{"short":"CC BY-NC (4.0)","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"ddc":["000"],"abstract":[{"lang":"eng","text":"We consider bidding games, a class of two-player zero-sum graph games. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit bids, and the higher bidder moves the token, where we break bidding ties in favor of Player 1. Player 1 wins the game iff the token visits a designated target vertex. We consider, for the first time, poorman discrete-bidding in which the granularity of the bids is restricted and the higher bid is paid to the bank. Previous work either did not impose granularity restrictions or considered Richman bidding (bids are paid to the opponent). While the latter mechanisms are technically more accessible, the former is more appealing from a practical standpoint. Our study focuses on threshold budgets, which is the necessary and sufficient initial budget required for Player 1 to ensure winning against a given Player 2 budget. We first show existence of thresholds. In DAGs, we show that threshold budgets can be approximated with error bounds by thresholds under continuous-bidding and that they exhibit a periodic behavior. We identify closed-form solutions in special cases. We implement and experiment with an algorithm to find threshold budgets."}],"external_id":{"arxiv":["2307.15218"]},"_id":"14518","file_date_updated":"2023-11-13T10:16:10Z","doi":"10.3233/FAIA230264","year":"2023","acknowledgement":"This research was supported in part by ISF grant no. 1679/21, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie Grant Agreement No. 665385.","date_created":"2023-11-12T23:00:56Z","citation":{"short":"G. Avni, T. Meggendorfer, S. Sadhukhan, J. Tkadlec, D. Zikelic, in:, Frontiers in Artificial Intelligence and Applications, IOS Press, 2023, pp. 141–148.","ama":"Avni G, Meggendorfer T, Sadhukhan S, Tkadlec J, Zikelic D. Reachability poorman discrete-bidding games. In: <i>Frontiers in Artificial Intelligence and Applications</i>. Vol 372. IOS Press; 2023:141-148. doi:<a href=\"https://doi.org/10.3233/FAIA230264\">10.3233/FAIA230264</a>","ieee":"G. Avni, T. Meggendorfer, S. Sadhukhan, J. Tkadlec, and D. Zikelic, “Reachability poorman discrete-bidding games,” in <i>Frontiers in Artificial Intelligence and Applications</i>, Krakow, Poland, 2023, vol. 372, pp. 141–148.","chicago":"Avni, Guy, Tobias Meggendorfer, Suman Sadhukhan, Josef Tkadlec, and Dorde Zikelic. “Reachability Poorman Discrete-Bidding Games.” In <i>Frontiers in Artificial Intelligence and Applications</i>, 372:141–48. IOS Press, 2023. <a href=\"https://doi.org/10.3233/FAIA230264\">https://doi.org/10.3233/FAIA230264</a>.","mla":"Avni, Guy, et al. “Reachability Poorman Discrete-Bidding Games.” <i>Frontiers in Artificial Intelligence and Applications</i>, vol. 372, IOS Press, 2023, pp. 141–48, doi:<a href=\"https://doi.org/10.3233/FAIA230264\">10.3233/FAIA230264</a>.","ista":"Avni G, Meggendorfer T, Sadhukhan S, Tkadlec J, Zikelic D. 2023. Reachability poorman discrete-bidding games. Frontiers in Artificial Intelligence and Applications. ECAI: European Conference on Artificial Intelligence vol. 372, 141–148.","apa":"Avni, G., Meggendorfer, T., Sadhukhan, S., Tkadlec, J., &#38; Zikelic, D. (2023). Reachability poorman discrete-bidding games. In <i>Frontiers in Artificial Intelligence and Applications</i> (Vol. 372, pp. 141–148). Krakow, Poland: IOS Press. <a href=\"https://doi.org/10.3233/FAIA230264\">https://doi.org/10.3233/FAIA230264</a>"},"ec_funded":1,"type":"conference","status":"public","arxiv":1,"author":[{"orcid":"0000-0001-5588-8287","id":"463C8BC2-F248-11E8-B48F-1D18A9856A87","last_name":"Avni","full_name":"Avni, Guy","first_name":"Guy"},{"full_name":"Meggendorfer, Tobias","first_name":"Tobias","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","last_name":"Meggendorfer","orcid":"0000-0002-1712-2165"},{"full_name":"Sadhukhan, Suman","first_name":"Suman","last_name":"Sadhukhan"},{"first_name":"Josef","full_name":"Tkadlec, Josef","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec","orcid":"0000-0002-1097-9684"},{"orcid":"0000-0002-4681-1699","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","first_name":"Dorde","full_name":"Zikelic, Dorde"}],"publication_identifier":{"issn":["0922-6389"],"isbn":["9781643684369"]},"month":"09","conference":{"location":"Krakow, Poland","end_date":"2023-10-04","name":"ECAI: European Conference on Artificial Intelligence","start_date":"2023-09-30"},"file":[{"file_name":"2023_FAIA_Avni.pdf","checksum":"1390ca38480fa4cf286b0f1a42e8c12f","file_id":"14529","success":1,"date_updated":"2023-11-13T10:16:10Z","date_created":"2023-11-13T10:16:10Z","creator":"dernst","content_type":"application/pdf","file_size":501011,"access_level":"open_access","relation":"main_file"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"28","oa_version":"Published Version","language":[{"iso":"eng"}],"publication":"Frontiers in Artificial Intelligence and Applications","article_processing_charge":"No","oa":1,"date_updated":"2025-07-14T09:09:57Z","title":"Reachability poorman discrete-bidding games","has_accepted_license":"1","scopus_import":"1","intvolume":"       372"},{"article_processing_charge":"No","date_updated":"2025-07-14T09:10:10Z","oa":1,"title":"Automated verification and control of infinite state stochastic systems","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["2663 - 337X"],"isbn":["978-3-99078-036-7"]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","file":[{"date_created":"2023-11-15T13:43:28Z","date_updated":"2023-11-15T13:43:28Z","success":1,"file_id":"14540","file_name":"main.pdf","checksum":"f23e002b0059ca78e1fbb864da52dd7e","content_type":"application/pdf","file_size":2116426,"access_level":"open_access","relation":"main_file","creator":"cchlebak"},{"creator":"cchlebak","content_type":"application/x-zip-compressed","relation":"source_file","access_level":"closed","file_size":35884057,"file_name":"thesis_source.zip","file_id":"14541","checksum":"80ca37618a3c7b59866875f8be9b15ed","date_created":"2023-11-15T13:44:24Z","date_updated":"2023-11-15T13:44:24Z"}],"day":"15","oa_version":"Published Version","author":[{"full_name":"Zikelic, Dorde","first_name":"Dorde","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699"}],"status":"public","type":"dissertation","alternative_title":["ISTA Thesis"],"related_material":{"record":[{"relation":"part_of_dissertation","id":"1194","status":"public"},{"id":"12000","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"12511","status":"public"},{"id":"14600","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"14601","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"9644","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"10414"}]},"degree_awarded":"PhD","ec_funded":1,"year":"2023","date_created":"2023-11-15T13:39:10Z","citation":{"chicago":"Zikelic, Dorde. “Automated Verification and Control of Infinite State Stochastic Systems.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/14539\">https://doi.org/10.15479/14539</a>.","ista":"Zikelic D. 2023. Automated verification and control of infinite state stochastic systems. Institute of Science and Technology Austria.","mla":"Zikelic, Dorde. <i>Automated Verification and Control of Infinite State Stochastic Systems</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/14539\">10.15479/14539</a>.","short":"D. Zikelic, Automated Verification and Control of Infinite State Stochastic Systems, Institute of Science and Technology Austria, 2023.","ama":"Zikelic D. Automated verification and control of infinite state stochastic systems. 2023. doi:<a href=\"https://doi.org/10.15479/14539\">10.15479/14539</a>","ieee":"D. Zikelic, “Automated verification and control of infinite state stochastic systems,” Institute of Science and Technology Austria, 2023.","apa":"Zikelic, D. (2023). <i>Automated verification and control of infinite state stochastic systems</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/14539\">https://doi.org/10.15479/14539</a>"},"doi":"10.15479/14539","_id":"14539","file_date_updated":"2023-11-15T13:44:24Z","tmp":{"image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"ddc":["000"],"abstract":[{"lang":"eng","text":"Stochastic systems provide a formal framework for modelling and quantifying uncertainty in systems and have been widely adopted in many application domains. Formal\r\nverification and control of finite state stochastic systems, a subfield of formal methods\r\nalso known as probabilistic model checking, is well studied. In contrast, formal verification and control of infinite state stochastic systems have received comparatively\r\nless attention. However, infinite state stochastic systems commonly arise in practice.\r\nFor instance, probabilistic models that contain continuous probability distributions such\r\nas normal or uniform, or stochastic dynamical systems which are a classical model for\r\ncontrol under uncertainty, both give rise to infinite state systems.\r\nThe goal of this thesis is to contribute to laying theoretical and algorithmic foundations\r\nof fully automated formal verification and control of infinite state stochastic systems,\r\nwith a particular focus on systems that may be executed over a long or infinite time.\r\nWe consider formal verification of infinite state stochastic systems in the setting of\r\nstatic analysis of probabilistic programs and formal control in the setting of controller\r\nsynthesis in stochastic dynamical systems. For both problems, we present some of the\r\nfirst fully automated methods for probabilistic (a.k.a. quantitative) reachability and\r\nsafety analysis applicable to infinite time horizon systems. We also advance the state\r\nof the art of probability 1 (a.k.a. qualitative) reachability analysis for both problems.\r\nFinally, for formal controller synthesis in stochastic dynamical systems, we present a\r\nnovel framework for learning neural network control policies in stochastic dynamical\r\nsystems with formal guarantees on correctness with respect to quantitative reachability,\r\nsafety or reach-avoid specifications.\r\n"}],"publication_status":"published","date_published":"2023-11-15T00:00:00Z","supervisor":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Institute of Science and Technology Austria","page":"256","department":[{"_id":"KrCh"},{"_id":"GradSch"}],"project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}]},{"type":"conference","status":"public","alternative_title":["LNCS"],"author":[{"last_name":"Ansaripour","full_name":"Ansaripour, Matin","first_name":"Matin"},{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2985-7724","first_name":"Thomas A","full_name":"Henzinger, Thomas A"},{"id":"3DC22916-F248-11E8-B48F-1D18A9856A87","last_name":"Lechner","full_name":"Lechner, Mathias","first_name":"Mathias"},{"full_name":"Zikelic, Dorde","first_name":"Dorde","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"22","oa_version":"None","publication_identifier":{"issn":["0302-9743"],"isbn":["9783031453281"],"eissn":["1611-3349"]},"month":"10","conference":{"start_date":"2023-10-24","name":"ATVA: Automated Technology for Verification and Analysis","end_date":"2023-10-27","location":"Singapore, Singapore"},"language":[{"iso":"eng"}],"publication":"21st International Symposium on Automated Technology for Verification and Analysis","title":"Learning provably stabilizing neural controllers for discrete-time stochastic systems","article_processing_charge":"No","date_updated":"2025-07-14T09:09:59Z","scopus_import":"1","intvolume":"     14215","project":[{"_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093","call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software"},{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","volume":14215,"department":[{"_id":"ToHe"},{"_id":"KrCh"}],"page":"357-379","date_published":"2023-10-22T00:00:00Z","publisher":"Springer Nature","publication_status":"published","abstract":[{"lang":"eng","text":"We consider the problem of learning control policies in discrete-time stochastic systems which guarantee that the system stabilizes within some specified stabilization region with probability 1. Our approach is based on the novel notion of stabilizing ranking supermartingales (sRSMs) that we introduce in this work. Our sRSMs overcome the limitation of methods proposed in previous works whose applicability is restricted to systems in which the stabilizing region cannot be left once entered under any control policy. We present a learning procedure that learns a control policy together with an sRSM that formally certifies probability 1 stability, both learned as neural networks. We show that this procedure can also be adapted to formally verifying that, under a given Lipschitz continuous control policy, the stochastic system stabilizes within some stabilizing region with probability 1. Our experimental evaluation shows that our learning procedure can successfully learn provably stabilizing policies in practice."}],"_id":"14559","doi":"10.1007/978-3-031-45329-8_17","date_created":"2023-11-19T23:00:56Z","citation":{"short":"M. Ansaripour, K. Chatterjee, T.A. Henzinger, M. Lechner, D. Zikelic, in:, 21st International Symposium on Automated Technology for Verification and Analysis, Springer Nature, 2023, pp. 357–379.","ama":"Ansaripour M, Chatterjee K, Henzinger TA, Lechner M, Zikelic D. Learning provably stabilizing neural controllers for discrete-time stochastic systems. In: <i>21st International Symposium on Automated Technology for Verification and Analysis</i>. Vol 14215. Springer Nature; 2023:357-379. doi:<a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">10.1007/978-3-031-45329-8_17</a>","ieee":"M. Ansaripour, K. Chatterjee, T. A. Henzinger, M. Lechner, and D. Zikelic, “Learning provably stabilizing neural controllers for discrete-time stochastic systems,” in <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, Singapore, Singapore, 2023, vol. 14215, pp. 357–379.","chicago":"Ansaripour, Matin, Krishnendu Chatterjee, Thomas A Henzinger, Mathias Lechner, and Dorde Zikelic. “Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems.” In <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, 14215:357–79. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">https://doi.org/10.1007/978-3-031-45329-8_17</a>.","ista":"Ansaripour M, Chatterjee K, Henzinger TA, Lechner M, Zikelic D. 2023. Learning provably stabilizing neural controllers for discrete-time stochastic systems. 21st International Symposium on Automated Technology for Verification and Analysis. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 14215, 357–379.","mla":"Ansaripour, Matin, et al. “Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems.” <i>21st International Symposium on Automated Technology for Verification and Analysis</i>, vol. 14215, Springer Nature, 2023, pp. 357–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">10.1007/978-3-031-45329-8_17</a>.","apa":"Ansaripour, M., Chatterjee, K., Henzinger, T. A., Lechner, M., &#38; Zikelic, D. (2023). Learning provably stabilizing neural controllers for discrete-time stochastic systems. In <i>21st International Symposium on Automated Technology for Verification and Analysis</i> (Vol. 14215, pp. 357–379). Singapore, Singapore: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-45329-8_17\">https://doi.org/10.1007/978-3-031-45329-8_17</a>"},"year":"2023","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","ec_funded":1},{"external_id":{"pmid":["38016637"]},"abstract":[{"lang":"eng","text":"Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader’s fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader’s dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader’s connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader’s fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident."}],"ddc":["000","570"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","department":[{"_id":"KrCh"}],"volume":20,"quality_controlled":"1","publisher":"The Royal Society","date_published":"2023-11-29T00:00:00Z","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"}],"ec_funded":1,"article_number":"20230355","citation":{"apa":"Tkadlec, J., Kaveh, K., Chatterjee, K., &#38; Nowak, M. A. (2023). Evolutionary dynamics of mutants that modify population structure. <i>Journal of the Royal Society, Interface</i>. The Royal Society. <a href=\"https://doi.org/10.1098/rsif.2023.0355\">https://doi.org/10.1098/rsif.2023.0355</a>","ieee":"J. Tkadlec, K. Kaveh, K. Chatterjee, and M. A. Nowak, “Evolutionary dynamics of mutants that modify population structure,” <i>Journal of the Royal Society, Interface</i>, vol. 20, no. 208. The Royal Society, 2023.","ama":"Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. Evolutionary dynamics of mutants that modify population structure. <i>Journal of the Royal Society, Interface</i>. 2023;20(208). doi:<a href=\"https://doi.org/10.1098/rsif.2023.0355\">10.1098/rsif.2023.0355</a>","short":"J. Tkadlec, K. Kaveh, K. Chatterjee, M.A. Nowak, Journal of the Royal Society, Interface 20 (2023).","mla":"Tkadlec, Josef, et al. “Evolutionary Dynamics of Mutants That Modify Population Structure.” <i>Journal of the Royal Society, Interface</i>, vol. 20, no. 208, 20230355, The Royal Society, 2023, doi:<a href=\"https://doi.org/10.1098/rsif.2023.0355\">10.1098/rsif.2023.0355</a>.","ista":"Tkadlec J, Kaveh K, Chatterjee K, Nowak MA. 2023. Evolutionary dynamics of mutants that modify population structure. Journal of the Royal Society, Interface. 20(208), 20230355.","chicago":"Tkadlec, Josef, Kamran Kaveh, Krishnendu Chatterjee, and Martin A. Nowak. “Evolutionary Dynamics of Mutants That Modify Population Structure.” <i>Journal of the Royal Society, Interface</i>. The Royal Society, 2023. <a href=\"https://doi.org/10.1098/rsif.2023.0355\">https://doi.org/10.1098/rsif.2023.0355</a>."},"date_created":"2023-12-10T23:00:58Z","acknowledgement":"K.C. acknowledges support from the ERC CoG 863818(ForM-SMArt). J.T. is supported by Center for Foundations ofModern Computer Science (Charles Univ. project UNCE/SCI/004).","year":"2023","doi":"10.1098/rsif.2023.0355","file_date_updated":"2023-12-11T11:10:32Z","_id":"14657","article_type":"original","oa_version":"Published Version","day":"29","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_name":"2023_RoyalInterface_Tkadlec.pdf","file_id":"14673","checksum":"2eefab13127c7786dbd33303c482a004","success":1,"date_updated":"2023-12-11T11:10:32Z","date_created":"2023-12-11T11:10:32Z","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_size":1720243}],"publication_identifier":{"eissn":["1742-5662"]},"month":"11","author":[{"last_name":"Tkadlec","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1097-9684","full_name":"Tkadlec, Josef","first_name":"Josef"},{"first_name":"Kamran","full_name":"Kaveh, Kamran","last_name":"Kaveh"},{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"full_name":"Nowak, Martin A.","first_name":"Martin A.","last_name":"Nowak"}],"pmid":1,"type":"journal_article","status":"public","has_accepted_license":"1","intvolume":"        20","scopus_import":"1","title":"Evolutionary dynamics of mutants that modify population structure","date_updated":"2025-07-14T09:10:00Z","oa":1,"article_processing_charge":"Yes (in subscription journal)","issue":"208","publication":"Journal of the Royal Society, Interface","language":[{"iso":"eng"}]},{"date_created":"2024-01-08T09:30:22Z","citation":{"apa":"Bastankhah, M., Chatterjee, K., Maddah-Ali, M. A., Schmid, S., Svoboda, J., &#38; Yeo, M. X. (2023). R2: Boosting liquidity in payment channel networks with online admission control. In <i>27th International Conference on Financial Cryptography and Data Security</i> (Vol. 13950, pp. 309–325). Bol, Brac, Croatia: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">https://doi.org/10.1007/978-3-031-47754-6_18</a>","short":"M. Bastankhah, K. Chatterjee, M.A. Maddah-Ali, S. Schmid, J. Svoboda, M.X. Yeo, in:, 27th International Conference on Financial Cryptography and Data Security, Springer Nature, 2023, pp. 309–325.","ama":"Bastankhah M, Chatterjee K, Maddah-Ali MA, Schmid S, Svoboda J, Yeo MX. R2: Boosting liquidity in payment channel networks with online admission control. In: <i>27th International Conference on Financial Cryptography and Data Security</i>. Vol 13950. Springer Nature; 2023:309-325. doi:<a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">10.1007/978-3-031-47754-6_18</a>","ieee":"M. Bastankhah, K. Chatterjee, M. A. Maddah-Ali, S. Schmid, J. Svoboda, and M. X. Yeo, “R2: Boosting liquidity in payment channel networks with online admission control,” in <i>27th International Conference on Financial Cryptography and Data Security</i>, Bol, Brac, Croatia, 2023, vol. 13950, pp. 309–325.","chicago":"Bastankhah, Mahsa, Krishnendu Chatterjee, Mohammad Ali Maddah-Ali, Stefan Schmid, Jakub Svoboda, and Michelle X Yeo. “R2: Boosting Liquidity in Payment Channel Networks with Online Admission Control.” In <i>27th International Conference on Financial Cryptography and Data Security</i>, 13950:309–25. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">https://doi.org/10.1007/978-3-031-47754-6_18</a>.","ista":"Bastankhah M, Chatterjee K, Maddah-Ali MA, Schmid S, Svoboda J, Yeo MX. 2023. R2: Boosting liquidity in payment channel networks with online admission control. 27th International Conference on Financial Cryptography and Data Security. FC: Financial Cryptography and Data Security, LNCS, vol. 13950, 309–325.","mla":"Bastankhah, Mahsa, et al. “R2: Boosting Liquidity in Payment Channel Networks with Online Admission Control.” <i>27th International Conference on Financial Cryptography and Data Security</i>, vol. 13950, Springer Nature, 2023, pp. 309–25, doi:<a href=\"https://doi.org/10.1007/978-3-031-47754-6_18\">10.1007/978-3-031-47754-6_18</a>."},"acknowledgement":"Supported by the German Federal Ministry of Education and Research (BMBF), grant 16KISK020K (6G-RIC), 2021–2025, and ERC CoG 863818 (ForM-SMArt).","year":"2023","ec_funded":1,"_id":"14736","doi":"10.1007/978-3-031-47754-6_18","publication_status":"published","abstract":[{"lang":"eng","text":"Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. PCNs, however, face the challenge that the frequent usage of certain routes may deplete channels in one direction, and hence prevent further transactions. In order to reap the full potential of PCNs, recharging and rebalancing mechanisms are required to provision channels, as well as an admission control logic to decide which transactions to reject in case capacity is insufficient. This paper presents a formal model of this optimisation problem. In particular, we consider an online algorithms perspective, where transactions arrive over time in an unpredictable manner. Our main contributions are competitive online algorithms which come with provable guarantees over time. We empirically evaluate our algorithms on randomly generated transactions to compare the average performance of our algorithms to our theoretical bounds. We also show how this model and approach differs from related problems in classic communication networks."}],"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"page":"309-325","department":[{"_id":"KrCh"},{"_id":"KrPi"}],"volume":13950,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-12-01T00:00:00Z","title":"R2: Boosting liquidity in payment channel networks with online admission control","date_updated":"2025-07-14T09:10:01Z","article_processing_charge":"No","intvolume":"     13950","language":[{"iso":"eng"}],"publication":"27th International Conference on Financial Cryptography and Data Security","author":[{"last_name":"Bastankhah","first_name":"Mahsa","full_name":"Bastankhah, Mahsa"},{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"last_name":"Maddah-Ali","full_name":"Maddah-Ali, Mohammad Ali","first_name":"Mohammad Ali"},{"last_name":"Schmid","first_name":"Stefan","full_name":"Schmid, Stefan"},{"first_name":"Jakub","full_name":"Svoboda, Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","orcid":"0000-0002-1419-3267"},{"full_name":"Yeo, Michelle X","first_name":"Michelle X","last_name":"Yeo","id":"2D82B818-F248-11E8-B48F-1D18A9856A87","orcid":"0009-0001-3676-4809"}],"day":"01","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"end_date":"2023-05-05","location":"Bol, Brac, Croatia","start_date":"2023-05-01","name":"FC: Financial Cryptography and Data Security"},"month":"12","publication_identifier":{"eissn":["1611-3349"],"eisbn":["9783031477546"],"isbn":["9783031477539"],"issn":["0302-9743"]},"alternative_title":["LNCS"],"status":"public","type":"conference"},{"doi":"10.1145/3585391","_id":"14778","article_type":"original","file_date_updated":"2024-01-16T08:11:24Z","related_material":{"record":[{"id":"10414","relation":"earlier_version","status":"public"}]},"article_number":"11","ec_funded":1,"year":"2023","acknowledgement":"This research was partially supported by the ERC CoG (grant no. 863818; ForM-SMArt), the Czech Science Foundation (grant no. GA21-24711S), and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 665385.","keyword":["Theoretical Computer Science","Software"],"date_created":"2024-01-10T09:27:43Z","citation":{"ista":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. 2023. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 35(2), 11.","mla":"Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>, vol. 35, no. 2, 11, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>.","chicago":"Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Dorde Zikelic. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>.","ama":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. 2023;35(2). doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>","ieee":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, and D. Zikelic, “On lexicographic proof rules for probabilistic termination,” <i>Formal Aspects of Computing</i>, vol. 35, no. 2. Association for Computing Machinery, 2023.","short":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, D. Zikelic, Formal Aspects of Computing 35 (2023).","apa":"Chatterjee, K., Kafshdar Goharshady, E., Novotný, P., Zárevúcky, J., &#38; Zikelic, D. (2023). On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>"},"date_published":"2023-06-23T00:00:00Z","publisher":"Association for Computing Machinery","quality_controlled":"1","volume":35,"department":[{"_id":"KrCh"}],"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["000"],"abstract":[{"text":"We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.","lang":"eng"}],"external_id":{"arxiv":["2108.02188"]},"publication_status":"published","publication":"Formal Aspects of Computing","language":[{"iso":"eng"}],"intvolume":"        35","has_accepted_license":"1","issue":"2","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2025-07-14T09:10:10Z","title":"On lexicographic proof rules for probabilistic termination","type":"journal_article","status":"public","publication_identifier":{"issn":["0934-5043"],"eissn":["1433-299X"]},"month":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2024-01-16T08:11:24Z","date_updated":"2024-01-16T08:11:24Z","success":1,"file_name":"2023_FormalAspectsComputing_Chatterjee.pdf","file_id":"14804","checksum":"3bb133eeb27ec01649a9a36445d952d9","content_type":"application/pdf","file_size":502522,"access_level":"open_access","relation":"main_file","creator":"dernst"}],"day":"23","oa_version":"Published Version","arxiv":1,"author":[{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"full_name":"Kafshdar Goharshady, Ehsan","first_name":"Ehsan","last_name":"Kafshdar Goharshady"},{"full_name":"Novotný, Petr","first_name":"Petr","last_name":"Novotný","id":"3CC3B868-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Zárevúcky","full_name":"Zárevúcky, Jiří","first_name":"Jiří"},{"orcid":"0000-0002-4681-1699","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","first_name":"Dorde","full_name":"Zikelic, Dorde"}]},{"department":[{"_id":"KrCh"}],"page":"231-264","quality_controlled":"1","volume":13,"publisher":"Springer Nature","date_published":"2023-03-01T00:00:00Z","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"external_id":{"isi":["000753777100001"]},"abstract":[{"lang":"eng","text":"Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings."}],"ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","doi":"10.1007/s13235-022-00425-3","file_date_updated":"2022-02-21T08:54:17Z","_id":"10770","article_type":"original","ec_funded":1,"date_created":"2022-02-20T23:01:32Z","citation":{"mla":"Graham, Thomas, et al. “Where Do Mistakes Lead? A Survey of Games with Incompetent Players.” <i>Dynamic Games and Applications</i>, vol. 13, Springer Nature, 2023, pp. 231–64, doi:<a href=\"https://doi.org/10.1007/s13235-022-00425-3\">10.1007/s13235-022-00425-3</a>.","ista":"Graham T, Kleshnina M, Filar JA. 2023. Where do mistakes lead? A survey of games with incompetent players. Dynamic Games and Applications. 13, 231–264.","chicago":"Graham, Thomas, Maria Kleshnina, and Jerzy A. Filar. “Where Do Mistakes Lead? A Survey of Games with Incompetent Players.” <i>Dynamic Games and Applications</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s13235-022-00425-3\">https://doi.org/10.1007/s13235-022-00425-3</a>.","short":"T. Graham, M. Kleshnina, J.A. Filar, Dynamic Games and Applications 13 (2023) 231–264.","ama":"Graham T, Kleshnina M, Filar JA. Where do mistakes lead? A survey of games with incompetent players. <i>Dynamic Games and Applications</i>. 2023;13:231-264. doi:<a href=\"https://doi.org/10.1007/s13235-022-00425-3\">10.1007/s13235-022-00425-3</a>","ieee":"T. Graham, M. Kleshnina, and J. A. Filar, “Where do mistakes lead? A survey of games with incompetent players,” <i>Dynamic Games and Applications</i>, vol. 13. Springer Nature, pp. 231–264, 2023.","apa":"Graham, T., Kleshnina, M., &#38; Filar, J. A. (2023). Where do mistakes lead? A survey of games with incompetent players. <i>Dynamic Games and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s13235-022-00425-3\">https://doi.org/10.1007/s13235-022-00425-3</a>"},"acknowledgement":"The authors would like to acknowledge stimulating email discussions with Dr Wayne Lobb of W.A. Lobb LLC on the topic of evolutionary games. We also thank Dr Thomas Taimre for his input to the material in Sect. 3.\r\nThe authors would like to acknowledge partial support from the Australian Research Council under the Discovery grant DP180101602 and support by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement #754411.","year":"2023","type":"journal_article","status":"public","day":"01","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"file_id":"10781","file_name":"2022_DynamicGamesApplic_Graham.pdf","checksum":"cd53b07e96f9030ddb348f305e5b58c7","date_created":"2022-02-21T08:54:17Z","date_updated":"2022-02-21T08:54:17Z","creator":"dernst","access_level":"open_access","file_size":1890512,"content_type":"application/pdf","relation":"main_file"}],"month":"03","publication_identifier":{"eissn":["2153-0793"],"issn":["2153-0785"]},"author":[{"full_name":"Graham, Thomas","first_name":"Thomas","last_name":"Graham"},{"id":"4E21749C-F248-11E8-B48F-1D18A9856A87","last_name":"Kleshnina","first_name":"Maria","full_name":"Kleshnina, Maria"},{"last_name":"Filar","first_name":"Jerzy A.","full_name":"Filar, Jerzy A."}],"publication":"Dynamic Games and Applications","language":[{"iso":"eng"}],"intvolume":"        13","has_accepted_license":"1","scopus_import":"1","isi":1,"title":"Where do mistakes lead? A survey of games with incompetent players","oa":1,"date_updated":"2023-10-04T09:24:30Z","article_processing_charge":"No"},{"status":"public","type":"conference","alternative_title":["LNCS"],"author":[{"last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","orcid":"0000-0002-1712-2165","full_name":"Meggendorfer, Tobias","first_name":"Tobias"}],"publication_identifier":{"isbn":["9783031199912"],"eissn":["1611-3349"],"eisbn":["9783031199929"],"issn":["0302-9743"]},"month":"10","conference":{"end_date":"2022-10-28","location":"Virtual","start_date":"2022-10-25","name":"ATVA: Automated Technology for Verification and Analysis"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"None","day":"21","language":[{"iso":"eng"}],"publication":"20th International Symposium on Automated Technology for Verification and Analysis","article_processing_charge":"No","date_updated":"2023-09-05T15:11:51Z","title":"PET – A partial exploration tool for probabilistic verification","scopus_import":"1","intvolume":"     13505","date_published":"2022-10-21T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":13505,"page":"320-326","department":[{"_id":"KrCh"}],"publication_status":"published","abstract":[{"text":"We present PET, a specialized and highly optimized framework for partial exploration on probabilistic systems. Over the last decade, several significant advances in the analysis of Markov decision processes employed partial exploration. In a nutshell, this idea allows to focus computation on specific parts of the system, guided by heuristics, while maintaining correctness. In particular, only relevant parts of the system are constructed on demand, which in turn potentially allows to omit constructing large parts of the system. Depending on the model, this leads to dramatic speed-ups, in extreme cases even up to an arbitrary factor. PET unifies several previous implementations and provides a flexible framework to easily implement partial exploration for many further problems. Our experimental evaluation shows significant improvements compared to the previous implementations while vastly reducing the overhead required to add support for additional properties.","lang":"eng"}],"_id":"12170","doi":"10.1007/978-3-031-19992-9_20","year":"2022","acknowledgement":"We thank Pranav Ashok and Maximilian Weininger for their contributions to spiritual predecessors of PET as well as motivating the initial development of this tool.","citation":{"chicago":"Meggendorfer, Tobias. “PET – A Partial Exploration Tool for Probabilistic Verification.” In <i>20th International Symposium on Automated Technology for Verification and Analysis</i>, 13505:320–26. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/978-3-031-19992-9_20\">https://doi.org/10.1007/978-3-031-19992-9_20</a>.","ista":"Meggendorfer T. 2022. PET – A partial exploration tool for probabilistic verification. 20th International Symposium on Automated Technology for Verification and Analysis. ATVA: Automated Technology for Verification and Analysis, LNCS, vol. 13505, 320–326.","mla":"Meggendorfer, Tobias. “PET – A Partial Exploration Tool for Probabilistic Verification.” <i>20th International Symposium on Automated Technology for Verification and Analysis</i>, vol. 13505, Springer Nature, 2022, pp. 320–26, doi:<a href=\"https://doi.org/10.1007/978-3-031-19992-9_20\">10.1007/978-3-031-19992-9_20</a>.","short":"T. Meggendorfer, in:, 20th International Symposium on Automated Technology for Verification and Analysis, Springer Nature, 2022, pp. 320–326.","ieee":"T. Meggendorfer, “PET – A partial exploration tool for probabilistic verification,” in <i>20th International Symposium on Automated Technology for Verification and Analysis</i>, Virtual, 2022, vol. 13505, pp. 320–326.","ama":"Meggendorfer T. PET – A partial exploration tool for probabilistic verification. In: <i>20th International Symposium on Automated Technology for Verification and Analysis</i>. Vol 13505. Springer Nature; 2022:320-326. doi:<a href=\"https://doi.org/10.1007/978-3-031-19992-9_20\">10.1007/978-3-031-19992-9_20</a>","apa":"Meggendorfer, T. (2022). PET – A partial exploration tool for probabilistic verification. In <i>20th International Symposium on Automated Technology for Verification and Analysis</i> (Vol. 13505, pp. 320–326). Virtual: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-19992-9_20\">https://doi.org/10.1007/978-3-031-19992-9_20</a>"},"date_created":"2023-01-12T12:11:07Z"},{"citation":{"chicago":"Chatterjee, Krishnendu, Jakub Svoboda, Dorde Zikelic, Andreas Pavlogiannis, and Josef Tkadlec. “Social Balance on Networks: Local Minima and Best-Edge Dynamics.” <i>Physical Review E</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/physreve.106.034321\">https://doi.org/10.1103/physreve.106.034321</a>.","ista":"Chatterjee K, Svoboda J, Zikelic D, Pavlogiannis A, Tkadlec J. 2022. Social balance on networks: Local minima and best-edge dynamics. Physical Review E. 106(3), 034321.","mla":"Chatterjee, Krishnendu, et al. “Social Balance on Networks: Local Minima and Best-Edge Dynamics.” <i>Physical Review E</i>, vol. 106, no. 3, 034321, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/physreve.106.034321\">10.1103/physreve.106.034321</a>.","ama":"Chatterjee K, Svoboda J, Zikelic D, Pavlogiannis A, Tkadlec J. Social balance on networks: Local minima and best-edge dynamics. <i>Physical Review E</i>. 2022;106(3). doi:<a href=\"https://doi.org/10.1103/physreve.106.034321\">10.1103/physreve.106.034321</a>","ieee":"K. Chatterjee, J. Svoboda, D. Zikelic, A. Pavlogiannis, and J. Tkadlec, “Social balance on networks: Local minima and best-edge dynamics,” <i>Physical Review E</i>, vol. 106, no. 3. American Physical Society, 2022.","short":"K. Chatterjee, J. Svoboda, D. Zikelic, A. Pavlogiannis, J. Tkadlec, Physical Review E 106 (2022).","apa":"Chatterjee, K., Svoboda, J., Zikelic, D., Pavlogiannis, A., &#38; Tkadlec, J. (2022). Social balance on networks: Local minima and best-edge dynamics. <i>Physical Review E</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physreve.106.034321\">https://doi.org/10.1103/physreve.106.034321</a>"},"date_created":"2023-01-16T09:57:57Z","year":"2022","acknowledgement":"K.C. acknowledges support from ERC Start Grant No. (279307: Graph Games), ERC Consolidator Grant No. (863818: ForM-SMart), and Austrian Science Fund (FWF)\r\nGrants No. P23499-N23 and No. S11407-N23 (RiSE). This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie\r\nSkłodowska-Curie Grant Agreement No. 665385.","article_number":"034321","ec_funded":1,"_id":"12257","article_type":"original","doi":"10.1103/physreve.106.034321","publication_status":"published","abstract":[{"text":"Structural balance theory is an established framework for studying social relationships of friendship and enmity. These relationships are modeled by a signed network whose energy potential measures the level of imbalance, while stochastic dynamics drives the network toward a state of minimum energy that captures social balance. It is known that this energy landscape has local minima that can trap socially aware dynamics, preventing it from reaching balance. Here we first study the robustness and attractor properties of these local minima. We show that a stochastic process can reach them from an abundance of initial states and that some local minima cannot be escaped by mild perturbations of the network. Motivated by these anomalies, we introduce best-edge dynamics (BED), a new plausible stochastic process. We prove that BED always reaches balance and that it does so fast in various interesting settings.","lang":"eng"}],"external_id":{"isi":["000870243100001"],"arxiv":["2210.02394"]},"project":[{"name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"},{"grant_number":"P 23499-N23","_id":"2584A770-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"_id":"25863FF4-B435-11E9-9278-68D0E5697425","grant_number":"S11407","name":"Game Theory","call_identifier":"FWF"},{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"volume":106,"quality_controlled":"1","department":[{"_id":"KrCh"}],"date_published":"2022-09-29T00:00:00Z","publisher":"American Physical Society","title":"Social balance on networks: Local minima and best-edge dynamics","article_processing_charge":"No","issue":"3","oa":1,"date_updated":"2025-07-14T09:09:49Z","scopus_import":"1","intvolume":"       106","isi":1,"language":[{"iso":"eng"}],"publication":"Physical Review E","arxiv":1,"author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee"},{"first_name":"Jakub","full_name":"Svoboda, Jakub","id":"130759D2-D7DD-11E9-87D2-DE0DE6697425","last_name":"Svoboda","orcid":"0000-0002-1419-3267"},{"full_name":"Zikelic, Dorde","first_name":"Dorde","orcid":"0000-0002-4681-1699","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Andreas","full_name":"Pavlogiannis, Andreas","orcid":"0000-0002-8943-0722","last_name":"Pavlogiannis","id":"49704004-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Tkadlec, Josef","first_name":"Josef","orcid":"0000-0002-1097-9684","id":"3F24CCC8-F248-11E8-B48F-1D18A9856A87","last_name":"Tkadlec"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.02394"}],"day":"29","publication_identifier":{"eissn":["2470-0053"],"issn":["2470-0045"]},"month":"09","status":"public","type":"journal_article"},{"article_type":"original","_id":"12280","file_date_updated":"2023-01-30T11:28:13Z","doi":"10.1371/journal.pcbi.1010149","year":"2022","acknowledgement":"This work was supported by the European Research Council (https://erc.europa.eu/)\r\nCoG 863818 (ForM-SMArt) (to K.C.), and the European Research Council Starting Grant 850529: E-DIRECT (to C.H.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.","keyword":["Computational Theory and Mathematics","Cellular and Molecular Neuroscience","Genetics","Molecular Biology","Ecology","Modeling and Simulation","Ecology","Evolution","Behavior and Systematics"],"date_created":"2023-01-16T10:02:51Z","citation":{"ama":"Schmid L, Hilbe C, Chatterjee K, Nowak M. Direct reciprocity between individuals that use different strategy spaces. <i>PLOS Computational Biology</i>. 2022;18(6). doi:<a href=\"https://doi.org/10.1371/journal.pcbi.1010149\">10.1371/journal.pcbi.1010149</a>","ieee":"L. Schmid, C. Hilbe, K. Chatterjee, and M. Nowak, “Direct reciprocity between individuals that use different strategy spaces,” <i>PLOS Computational Biology</i>, vol. 18, no. 6. Public Library of Science, 2022.","short":"L. Schmid, C. Hilbe, K. Chatterjee, M. Nowak, PLOS Computational Biology 18 (2022).","ista":"Schmid L, Hilbe C, Chatterjee K, Nowak M. 2022. Direct reciprocity between individuals that use different strategy spaces. PLOS Computational Biology. 18(6), e1010149.","mla":"Schmid, Laura, et al. “Direct Reciprocity between Individuals That Use Different Strategy Spaces.” <i>PLOS Computational Biology</i>, vol. 18, no. 6, e1010149, Public Library of Science, 2022, doi:<a href=\"https://doi.org/10.1371/journal.pcbi.1010149\">10.1371/journal.pcbi.1010149</a>.","chicago":"Schmid, Laura, Christian Hilbe, Krishnendu Chatterjee, and Martin Nowak. “Direct Reciprocity between Individuals That Use Different Strategy Spaces.” <i>PLOS Computational Biology</i>. Public Library of Science, 2022. <a href=\"https://doi.org/10.1371/journal.pcbi.1010149\">https://doi.org/10.1371/journal.pcbi.1010149</a>.","apa":"Schmid, L., Hilbe, C., Chatterjee, K., &#38; Nowak, M. (2022). Direct reciprocity between individuals that use different strategy spaces. <i>PLOS Computational Biology</i>. Public Library of Science. <a href=\"https://doi.org/10.1371/journal.pcbi.1010149\">https://doi.org/10.1371/journal.pcbi.1010149</a>"},"article_number":"e1010149","ec_funded":1,"project":[{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818"}],"date_published":"2022-06-14T00:00:00Z","publisher":"Public Library of Science","volume":18,"quality_controlled":"1","department":[{"_id":"KrCh"}],"publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["000","570"],"abstract":[{"lang":"eng","text":"In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate."}],"external_id":{"pmid":["35700167"],"isi":["000843626800031"]},"language":[{"iso":"eng"}],"publication":"PLOS Computational Biology","issue":"6","article_processing_charge":"No","date_updated":"2025-07-14T09:09:49Z","oa":1,"title":"Direct reciprocity between individuals that use different strategy spaces","isi":1,"intvolume":"        18","has_accepted_license":"1","scopus_import":"1","type":"journal_article","status":"public","pmid":1,"author":[{"last_name":"Schmid","id":"38B437DE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6978-7329","full_name":"Schmid, Laura","first_name":"Laura"},{"full_name":"Hilbe, Christian","first_name":"Christian","orcid":"0000-0001-5116-955X","last_name":"Hilbe","id":"2FDF8F3C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","orcid":"0000-0002-4561-241X"},{"last_name":"Nowak","first_name":"Martin","full_name":"Nowak, Martin"}],"publication_identifier":{"eissn":["1553-7358"]},"month":"06","file":[{"date_created":"2023-01-30T11:28:13Z","date_updated":"2023-01-30T11:28:13Z","success":1,"file_name":"2022_PlosCompBio_Schmid.pdf","checksum":"31b6b311b6731f1658277a9dfff6632c","file_id":"12460","access_level":"open_access","file_size":3143222,"content_type":"application/pdf","relation":"main_file","creator":"dernst"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","day":"14"},{"doi":"10.1609/aaai.v36i7.20695","_id":"12511","article_type":"original","related_material":{"record":[{"relation":"dissertation_contains","id":"14539","status":"public"}]},"ec_funded":1,"keyword":["General Medicine"],"citation":{"apa":"Lechner, M., Zikelic, D., Chatterjee, K., &#38; Henzinger, T. A. (2022). Stability verification in stochastic control systems via neural network supermartingales. <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v36i7.20695\">https://doi.org/10.1609/aaai.v36i7.20695</a>","ieee":"M. Lechner, D. Zikelic, K. Chatterjee, and T. A. Henzinger, “Stability verification in stochastic control systems via neural network supermartingales,” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, vol. 36, no. 7. Association for the Advancement of Artificial Intelligence, pp. 7326–7336, 2022.","ama":"Lechner M, Zikelic D, Chatterjee K, Henzinger TA. Stability verification in stochastic control systems via neural network supermartingales. <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. 2022;36(7):7326-7336. doi:<a href=\"https://doi.org/10.1609/aaai.v36i7.20695\">10.1609/aaai.v36i7.20695</a>","short":"M. Lechner, D. Zikelic, K. Chatterjee, T.A. Henzinger, Proceedings of the AAAI Conference on Artificial Intelligence 36 (2022) 7326–7336.","ista":"Lechner M, Zikelic D, Chatterjee K, Henzinger TA. 2022. Stability verification in stochastic control systems via neural network supermartingales. Proceedings of the AAAI Conference on Artificial Intelligence. 36(7), 7326–7336.","mla":"Lechner, Mathias, et al. “Stability Verification in Stochastic Control Systems via Neural Network Supermartingales.” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>, vol. 36, no. 7, Association for the Advancement of Artificial Intelligence, 2022, pp. 7326–36, doi:<a href=\"https://doi.org/10.1609/aaai.v36i7.20695\">10.1609/aaai.v36i7.20695</a>.","chicago":"Lechner, Mathias, Dorde Zikelic, Krishnendu Chatterjee, and Thomas A Henzinger. “Stability Verification in Stochastic Control Systems via Neural Network Supermartingales.” <i>Proceedings of the AAAI Conference on Artificial Intelligence</i>. Association for the Advancement of Artificial Intelligence, 2022. <a href=\"https://doi.org/10.1609/aaai.v36i7.20695\">https://doi.org/10.1609/aaai.v36i7.20695</a>."},"date_created":"2023-02-05T17:29:50Z","year":"2022","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093, ERC CoG 863818 (FoRM-SMArt) and the European Union’s Horizon 2020 research and innovation programme\r\nunder the Marie Skłodowska-Curie Grant Agreement No. 665385.","quality_controlled":"1","volume":36,"page":"7326-7336","department":[{"_id":"ToHe"},{"_id":"KrCh"}],"date_published":"2022-06-28T00:00:00Z","publisher":"Association for the Advancement of Artificial Intelligence","project":[{"name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020","grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d"},{"call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program"}],"abstract":[{"lang":"eng","text":"We consider the problem of formally verifying almost-sure (a.s.) asymptotic stability in discrete-time nonlinear stochastic control systems. While verifying stability in deterministic control systems is extensively studied in the literature, verifying stability in stochastic control systems is an open problem. The few existing works on this topic either consider only specialized forms of stochasticity or make restrictive assumptions on the system, rendering them inapplicable to learning algorithms with neural network policies. \r\n In this work, we present an approach for general nonlinear stochastic control problems with two novel aspects: (a) instead of classical stochastic extensions of Lyapunov functions, we use ranking supermartingales (RSMs) to certify a.s. asymptotic stability, and (b) we present a method for learning neural network RSMs. \r\n We prove that our approach guarantees a.s. asymptotic stability of the system and\r\n provides the first method to obtain bounds on the stabilization time, which stochastic Lyapunov functions do not.\r\n Finally, we validate our approach experimentally on a set of nonlinear stochastic reinforcement learning environments with neural network policies."}],"external_id":{"arxiv":["2112.09495"]},"publication_status":"published","publication":"Proceedings of the AAAI Conference on Artificial Intelligence","language":[{"iso":"eng"}],"intvolume":"        36","scopus_import":"1","title":"Stability verification in stochastic control systems via neural network supermartingales","issue":"7","article_processing_charge":"No","date_updated":"2025-07-14T09:09:58Z","oa":1,"status":"public","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/2112.09495","open_access":"1"}],"day":"28","oa_version":"Preprint","month":"06","publication_identifier":{"eissn":["2374-3468"],"isbn":["9781577358350"],"issn":["2159-5399"]},"arxiv":1,"author":[{"first_name":"Mathias","full_name":"Lechner, Mathias","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","last_name":"Lechner"},{"last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde"},{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"full_name":"Henzinger, Thomas A","first_name":"Thomas A","last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2985-7724"}]},{"author":[{"last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1","orcid":"0000-0002-1712-2165","first_name":"Tobias","full_name":"Meggendorfer, Tobias"}],"arxiv":1,"conference":{"end_date":"2022-03-01","location":"Virtual","start_date":"2022-02-22","name":"Conference on Artificial Intelligence"},"publication_identifier":{"eissn":["2374-3468"],"isbn":["1577358767"]},"month":"06","oa_version":"Preprint","day":"28","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2203.01640"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"conference","date_updated":"2023-02-20T07:19:12Z","oa":1,"article_processing_charge":"No","issue":"9","title":"Risk-aware stochastic shortest path","intvolume":"        36","scopus_import":"1","language":[{"iso":"eng"}],"publication":"Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022","publication_status":"published","external_id":{"arxiv":["2203.01640"]},"abstract":[{"lang":"eng","text":"We treat the problem of risk-aware control for stochastic shortest path (SSP) on Markov decision processes (MDP). Typically, expectation is considered for SSP, which however is oblivious to the incurred risk. We present an alternative view, instead optimizing conditional value-at-risk (CVaR), an established risk measure. We treat both Markov chains as well as MDP and introduce, through novel insights, two algorithms, based on linear programming and value iteration, respectively. Both algorithms offer precise and provably correct solutions. Evaluation of our prototype implementation shows that risk-aware control is feasible on several moderately sized models."}],"publisher":"Association for the Advancement of Artificial Intelligence","date_published":"2022-06-28T00:00:00Z","page":"9858-9867","department":[{"_id":"KrCh"}],"quality_controlled":"1","volume":36,"year":"2022","date_created":"2023-02-19T23:00:56Z","citation":{"apa":"Meggendorfer, T. (2022). Risk-aware stochastic shortest path. In <i>Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022</i> (Vol. 36, pp. 9858–9867). Virtual: Association for the Advancement of Artificial Intelligence. <a href=\"https://doi.org/10.1609/aaai.v36i9.21222\">https://doi.org/10.1609/aaai.v36i9.21222</a>","ama":"Meggendorfer T. Risk-aware stochastic shortest path. In: <i>Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022</i>. Vol 36. Association for the Advancement of Artificial Intelligence; 2022:9858-9867. doi:<a href=\"https://doi.org/10.1609/aaai.v36i9.21222\">10.1609/aaai.v36i9.21222</a>","ieee":"T. Meggendorfer, “Risk-aware stochastic shortest path,” in <i>Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022</i>, Virtual, 2022, vol. 36, no. 9, pp. 9858–9867.","short":"T. Meggendorfer, in:, Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022, Association for the Advancement of Artificial Intelligence, 2022, pp. 9858–9867.","ista":"Meggendorfer T. 2022. Risk-aware stochastic shortest path. Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022. Conference on Artificial Intelligence vol. 36, 9858–9867.","chicago":"Meggendorfer, Tobias. “Risk-Aware Stochastic Shortest Path.” In <i>Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022</i>, 36:9858–67. Association for the Advancement of Artificial Intelligence, 2022. <a href=\"https://doi.org/10.1609/aaai.v36i9.21222\">https://doi.org/10.1609/aaai.v36i9.21222</a>.","mla":"Meggendorfer, Tobias. “Risk-Aware Stochastic Shortest Path.” <i>Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022</i>, vol. 36, no. 9, Association for the Advancement of Artificial Intelligence, 2022, pp. 9858–67, doi:<a href=\"https://doi.org/10.1609/aaai.v36i9.21222\">10.1609/aaai.v36i9.21222</a>."},"_id":"12568","doi":"10.1609/aaai.v36i9.21222"},{"article_number":"2209.14368","ec_funded":1,"date_created":"2023-02-24T12:21:40Z","title":"Repeated prophet inequality with near-optimal bounds","citation":{"apa":"Chatterjee, K., Mohammadi, M., &#38; Saona Urmeneta, R. J. (n.d.). Repeated prophet inequality with near-optimal bounds. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2209.14368\">https://doi.org/10.48550/ARXIV.2209.14368</a>","chicago":"Chatterjee, Krishnendu, Mona Mohammadi, and Raimundo J Saona Urmeneta. “Repeated Prophet Inequality with Near-Optimal Bounds.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2209.14368\">https://doi.org/10.48550/ARXIV.2209.14368</a>.","mla":"Chatterjee, Krishnendu, et al. “Repeated Prophet Inequality with Near-Optimal Bounds.” <i>ArXiv</i>, 2209.14368, doi:<a href=\"https://doi.org/10.48550/ARXIV.2209.14368\">10.48550/ARXIV.2209.14368</a>.","ista":"Chatterjee K, Mohammadi M, Saona Urmeneta RJ. Repeated prophet inequality with near-optimal bounds. arXiv, 2209.14368.","short":"K. Chatterjee, M. Mohammadi, R.J. Saona Urmeneta, ArXiv (n.d.).","ieee":"K. Chatterjee, M. Mohammadi, and R. J. Saona Urmeneta, “Repeated prophet inequality with near-optimal bounds,” <i>arXiv</i>. .","ama":"Chatterjee K, Mohammadi M, Saona Urmeneta RJ. Repeated prophet inequality with near-optimal bounds. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2209.14368\">10.48550/ARXIV.2209.14368</a>"},"year":"2022","article_processing_charge":"No","acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt) grant.","date_updated":"2025-07-14T09:09:51Z","oa":1,"doi":"10.48550/ARXIV.2209.14368","publication":"arXiv","_id":"12677","language":[{"iso":"eng"}],"abstract":[{"text":"In modern sample-driven Prophet Inequality, an adversary chooses a sequence of n items with values v1,v2,…,vn to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase), some items, possibly selected at random, are revealed to the DM, but she can never accept them. In the second phase, the DM is presented with the other items in a random order and online fashion. For each item, she must make an irrevocable decision to either accept the item and stop the process or reject the item forever and proceed to the next item. The goal of the DM is to maximize the expected value as compared to a Prophet (or offline algorithm) that has access to all information. In this setting, the sampling phase has no cost and is not part of the optimization process. However, in many scenarios, the samples are obtained as part of the decision-making process.\r\nWe model this aspect as a two-phase Prophet Inequality where an adversary chooses a sequence of 2n items with values v1,v2,…,v2n and the items are randomly ordered. Finally, there are two phases of the Prophet Inequality problem with the first n-items and the rest of the items, respectively. We show that some basic algorithms achieve a ratio of at most 0.450. We present an algorithm that achieves a ratio of at least 0.495. Finally, we show that for every algorithm the ratio it can achieve is at most 0.502. Hence our algorithm is near-optimal.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","external_id":{"arxiv":["2209.14368"]},"day":"28","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2209.14368"}],"month":"09","arxiv":1,"author":[{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"id":"4363614d-b686-11ed-a7d5-ac9e4a24bc2e","last_name":"Mohammadi","first_name":"Mona","full_name":"Mohammadi, Mona"},{"first_name":"Raimundo J","full_name":"Saona Urmeneta, Raimundo J","orcid":"0000-0001-5103-038X","last_name":"Saona Urmeneta","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425"}],"publication_status":"submitted","department":[{"_id":"GradSch"},{"_id":"KrCh"}],"type":"preprint","status":"public","date_published":"2022-09-28T00:00:00Z","project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"}]},{"intvolume":"       243","scopus_import":"1","has_accepted_license":"1","oa":1,"date_updated":"2023-09-26T10:43:30Z","article_processing_charge":"No","title":"Anytime guarantees for reachability in uncountable Markov decision processes","publication":"33rd International Conference on Concurrency Theory ","language":[{"iso":"eng"}],"conference":{"start_date":"2022-09-13","name":"CONCUR: Conference on Concurrency Theory","end_date":"2022-09-16","location":"Warsaw, Poland"},"publication_identifier":{"issn":["1868-8969"]},"month":"09","oa_version":"Published Version","day":"15","file":[{"date_updated":"2023-09-26T10:43:15Z","date_created":"2023-09-26T10:43:15Z","file_id":"14372","file_name":"2022_LIPIcS_Grover.pdf","checksum":"e282e43d3ae0ba6e067b72f4583e13c0","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_size":960036,"creator":"dernst"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Grover","first_name":"Kush","full_name":"Grover, Kush"},{"full_name":"Kretinsky, Jan","first_name":"Jan","orcid":"0000-0002-8122-2881","id":"44CEF464-F248-11E8-B48F-1D18A9856A87","last_name":"Kretinsky"},{"first_name":"Tobias","full_name":"Meggendorfer, Tobias","orcid":"0000-0002-1712-2165","last_name":"Meggendorfer","id":"b21b0c15-30a2-11eb-80dc-f13ca25802e1"},{"full_name":"Weininger, Maimilian","first_name":"Maimilian","last_name":"Weininger"}],"arxiv":1,"alternative_title":["LIPIcs"],"status":"public","type":"conference","article_number":"11","acknowledgement":"Kush Grover: The author has been supported by the DFG research training group GRK\r\n2428 ConVeY.\r\nMaximilian Weininger: The author has been partially supported by DFG projects 383882557\r\nStatistical Unbounded Verification (SUV) and 427755713 Group-By Objectives in Probabilistic\r\nVerification (GOPro)","year":"2022","citation":{"apa":"Grover, K., Kretinsky, J., Meggendorfer, T., &#38; Weininger, M. (2022). Anytime guarantees for reachability in uncountable Markov decision processes. In <i>33rd International Conference on Concurrency Theory </i> (Vol. 243). Warsaw, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">https://doi.org/10.4230/LIPIcs.CONCUR.2022.11</a>","mla":"Grover, Kush, et al. “Anytime Guarantees for Reachability in Uncountable Markov Decision Processes.” <i>33rd International Conference on Concurrency Theory </i>, vol. 243, 11, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">10.4230/LIPIcs.CONCUR.2022.11</a>.","chicago":"Grover, Kush, Jan Kretinsky, Tobias Meggendorfer, and Maimilian Weininger. “Anytime Guarantees for Reachability in Uncountable Markov Decision Processes.” In <i>33rd International Conference on Concurrency Theory </i>, Vol. 243. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">https://doi.org/10.4230/LIPIcs.CONCUR.2022.11</a>.","ista":"Grover K, Kretinsky J, Meggendorfer T, Weininger M. 2022. Anytime guarantees for reachability in uncountable Markov decision processes. 33rd International Conference on Concurrency Theory . CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 243, 11.","ieee":"K. Grover, J. Kretinsky, T. Meggendorfer, and M. Weininger, “Anytime guarantees for reachability in uncountable Markov decision processes,” in <i>33rd International Conference on Concurrency Theory </i>, Warsaw, Poland, 2022, vol. 243.","ama":"Grover K, Kretinsky J, Meggendorfer T, Weininger M. Anytime guarantees for reachability in uncountable Markov decision processes. In: <i>33rd International Conference on Concurrency Theory </i>. Vol 243. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2022.11\">10.4230/LIPIcs.CONCUR.2022.11</a>","short":"K. Grover, J. Kretinsky, T. Meggendorfer, M. Weininger, in:, 33rd International Conference on Concurrency Theory , Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022."},"date_created":"2023-03-28T08:09:32Z","doi":"10.4230/LIPIcs.CONCUR.2022.11","file_date_updated":"2023-09-26T10:43:15Z","_id":"12775","ddc":["000"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["2008.04824"]},"abstract":[{"lang":"eng","text":"We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a sequence of approximations converging to the true value in the limit, our aim is to obtain an algorithm with guarantees on the precision of the approximation.\r\nAs this problem is undecidable in general, assumptions on the MDP are necessary. Our main contribution is to identify sufficient assumptions that are as weak as possible, thus approaching the \"boundary\" of which systems can be correctly and reliably analyzed. To this end, we also argue why each of our assumptions is necessary for algorithms based on processing finitely many observations.\r\nWe present two solution variants. The first one provides converging lower bounds under weaker assumptions than typical ones from previous works concerned with guarantees. The second one then utilizes stronger assumptions to additionally provide converging upper bounds. Altogether, we obtain an anytime algorithm, i.e. yielding a sequence of approximants with known and iteratively improving precision, converging to the true value in the limit. Besides, due to the generality of our assumptions, our algorithms are very general templates, readily allowing for various heuristics from literature in contrast to, e.g., a specific discretization algorithm. Our theoretical contribution thus paves the way for future practical improvements without sacrificing correctness guarantees."}],"publication_status":"published","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","date_published":"2022-09-15T00:00:00Z","department":[{"_id":"KrCh"}],"volume":243,"quality_controlled":"1"},{"language":[{"iso":"eng"}],"publication":"Mathematics of Operations Research","oa":1,"date_updated":"2023-09-05T13:16:11Z","issue":"1","article_processing_charge":"No","title":"Finite-memory strategies in POMDPs with long-run average objectives","isi":1,"intvolume":"        47","scopus_import":"1","type":"journal_article","status":"public","author":[{"last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"last_name":"Saona Urmeneta","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425","orcid":"0000-0001-5103-038X","first_name":"Raimundo J","full_name":"Saona Urmeneta, Raimundo J"},{"full_name":"Ziliotto, Bruno","first_name":"Bruno","last_name":"Ziliotto"}],"arxiv":1,"publication_identifier":{"issn":["0364-765X"],"eissn":["1526-5471"]},"month":"02","oa_version":"Preprint","day":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1904.13360"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9311","article_type":"original","doi":"10.1287/moor.2020.1116","acknowledgement":"Partially supported by Austrian Science Fund (FWF) NFN Grant No RiSE/SHiNE S11407, by CONICYT Chile through grant PII 20150140, and by ECOS-CONICYT through grant C15E03.\r\n","year":"2022","date_created":"2021-04-08T09:33:31Z","citation":{"short":"K. Chatterjee, R.J. Saona Urmeneta, B. Ziliotto, Mathematics of Operations Research 47 (2022) 100–119.","ieee":"K. Chatterjee, R. J. Saona Urmeneta, and B. Ziliotto, “Finite-memory strategies in POMDPs with long-run average objectives,” <i>Mathematics of Operations Research</i>, vol. 47, no. 1. Institute for Operations Research and the Management Sciences, pp. 100–119, 2022.","ama":"Chatterjee K, Saona Urmeneta RJ, Ziliotto B. Finite-memory strategies in POMDPs with long-run average objectives. <i>Mathematics of Operations Research</i>. 2022;47(1):100-119. doi:<a href=\"https://doi.org/10.1287/moor.2020.1116\">10.1287/moor.2020.1116</a>","chicago":"Chatterjee, Krishnendu, Raimundo J Saona Urmeneta, and Bruno Ziliotto. “Finite-Memory Strategies in POMDPs with Long-Run Average Objectives.” <i>Mathematics of Operations Research</i>. Institute for Operations Research and the Management Sciences, 2022. <a href=\"https://doi.org/10.1287/moor.2020.1116\">https://doi.org/10.1287/moor.2020.1116</a>.","mla":"Chatterjee, Krishnendu, et al. “Finite-Memory Strategies in POMDPs with Long-Run Average Objectives.” <i>Mathematics of Operations Research</i>, vol. 47, no. 1, Institute for Operations Research and the Management Sciences, 2022, pp. 100–19, doi:<a href=\"https://doi.org/10.1287/moor.2020.1116\">10.1287/moor.2020.1116</a>.","ista":"Chatterjee K, Saona Urmeneta RJ, Ziliotto B. 2022. Finite-memory strategies in POMDPs with long-run average objectives. Mathematics of Operations Research. 47(1), 100–119.","apa":"Chatterjee, K., Saona Urmeneta, R. J., &#38; Ziliotto, B. (2022). Finite-memory strategies in POMDPs with long-run average objectives. <i>Mathematics of Operations Research</i>. Institute for Operations Research and the Management Sciences. <a href=\"https://doi.org/10.1287/moor.2020.1116\">https://doi.org/10.1287/moor.2020.1116</a>"},"keyword":["Management Science and Operations Research","General Mathematics","Computer Science Applications"],"project":[{"call_identifier":"FWF","name":"Game Theory","grant_number":"S11407","_id":"25863FF4-B435-11E9-9278-68D0E5697425"}],"publisher":"Institute for Operations Research and the Management Sciences","date_published":"2022-02-01T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"KrCh"}],"page":"100-119","volume":47,"quality_controlled":"1","publication_status":"published","external_id":{"arxiv":["1904.13360"],"isi":["000731918100001"]},"abstract":[{"text":"Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the decision maker has approximately optimal strategies with finite memory. This implies notably that approximating the long-run value is recursively enumerable, as well as a weak continuity property of the value with respect to the transition function. ","lang":"eng"}]},{"citation":{"apa":"Zikelic, D., Lechner, M., Henzinger, T. A., &#38; Chatterjee, K. (n.d.). Learning control policies for stochastic systems with reach-avoid guarantees. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">https://doi.org/10.48550/ARXIV.2210.05308</a>","ista":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. arXiv, <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>.","mla":"Zikelic, Dorde, et al. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>.","chicago":"Zikelic, Dorde, Mathias Lechner, Thomas A Henzinger, and Krishnendu Chatterjee. “Learning Control Policies for Stochastic Systems with Reach-Avoid Guarantees.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">https://doi.org/10.48550/ARXIV.2210.05308</a>.","ama":"Zikelic D, Lechner M, Henzinger TA, Chatterjee K. Learning control policies for stochastic systems with reach-avoid guarantees. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/ARXIV.2210.05308\">10.48550/ARXIV.2210.05308</a>","ieee":"D. Zikelic, M. Lechner, T. A. Henzinger, and K. Chatterjee, “Learning control policies for stochastic systems with reach-avoid guarantees,” <i>arXiv</i>. .","short":"D. Zikelic, M. Lechner, T.A. Henzinger, K. Chatterjee, ArXiv (n.d.)."},"date_created":"2023-11-24T13:10:09Z","title":"Learning control policies for stochastic systems with reach-avoid guarantees","article_processing_charge":"No","year":"2022","oa":1,"date_updated":"2025-07-14T09:10:02Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"14539"},{"relation":"later_version","id":"14830","status":"public"}]},"ec_funded":1,"_id":"14600","language":[{"iso":"eng"}],"doi":"10.48550/ARXIV.2210.05308","publication":"arXiv","arxiv":1,"author":[{"last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde"},{"last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87","first_name":"Mathias","full_name":"Lechner, Mathias"},{"orcid":"0000-0002-2985-7724","last_name":"Henzinger","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A"},{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"}],"publication_status":"submitted","abstract":[{"text":"We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and generalize stability and safety guarantees, with a tolerable probability threshold $p\\in[0,1]$ over the infinite time horizon. Our method leverages advances in machine learning literature and it represents formal certificates as neural networks. In particular, we learn a certificate in the form of a reach-avoid supermartingale (RASM), a novel notion that we introduce in this work. Our RASMs provide reachability and avoidance guarantees by imposing constraints on what can be viewed as a stochastic extension of level sets of Lyapunov functions for deterministic systems. Our approach solves several important problems -- it can be used to learn a control policy from scratch, to verify a reach-avoid specification for a fixed control policy, or to fine-tune a pre-trained policy if it does not satisfy the reach-avoid specification. We validate our approach on $3$ stochastic non-linear reinforcement learning tasks.","lang":"eng"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","external_id":{"arxiv":["2210.05308"]},"oa_version":"Preprint","day":"29","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2210.05308"}],"tmp":{"short":"CC BY-SA (4.0)","name":"Creative Commons Attribution-ShareAlike 4.0 International Public License (CC BY-SA 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","image":"/images/cc_by_sa.png"},"month":"11","project":[{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020"},{"call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"department":[{"_id":"KrCh"},{"_id":"ToHe"}],"status":"public","license":"https://creativecommons.org/licenses/by-sa/4.0/","type":"preprint","date_published":"2022-11-29T00:00:00Z"},{"project":[{"_id":"62781420-2b32-11ec-9570-8d9b63373d4d","grant_number":"101020093","name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020"},{"grant_number":"863818","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","call_identifier":"H2020","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"date_published":"2022-05-24T00:00:00Z","type":"preprint","status":"public","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"arxiv":1,"publication_status":"submitted","author":[{"id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","last_name":"Zikelic","orcid":"0000-0002-4681-1699","first_name":"Dorde","full_name":"Zikelic, Dorde"},{"full_name":"Lechner, Mathias","first_name":"Mathias","last_name":"Lechner","id":"3DC22916-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4561-241X","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","orcid":"0000-0002-2985-7724","first_name":"Thomas A","full_name":"Henzinger, Thomas A"}],"month":"05","abstract":[{"lang":"eng","text":"In this work, we address the problem of learning provably stable neural\r\nnetwork policies for stochastic control systems. While recent work has\r\ndemonstrated the feasibility of certifying given policies using martingale\r\ntheory, the problem of how to learn such policies is little explored. Here, we\r\nstudy the effectiveness of jointly learning a policy together with a martingale\r\ncertificate that proves its stability using a single learning algorithm. We\r\nobserve that the joint optimization problem becomes easily stuck in local\r\nminima when starting from a randomly initialized policy. Our results suggest\r\nthat some form of pre-training of the policy is required for the joint\r\noptimization to repair and verify the policy successfully."}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2205.11991"}],"day":"24","oa_version":"Preprint","external_id":{"arxiv":["2205.11991"]},"language":[{"iso":"eng"}],"_id":"14601","publication":"arXiv","doi":"10.48550/arXiv.2205.11991","year":"2022","article_processing_charge":"No","date_updated":"2025-07-14T09:10:00Z","oa":1,"title":"Learning stabilizing policies in stochastic control systems","citation":{"apa":"Zikelic, D., Lechner, M., Chatterjee, K., &#38; Henzinger, T. A. (n.d.). Learning stabilizing policies in stochastic control systems. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2205.11991\">https://doi.org/10.48550/arXiv.2205.11991</a>","mla":"Zikelic, Dorde, et al. “Learning Stabilizing Policies in Stochastic Control Systems.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2205.11991\">10.48550/arXiv.2205.11991</a>.","chicago":"Zikelic, Dorde, Mathias Lechner, Krishnendu Chatterjee, and Thomas A Henzinger. “Learning Stabilizing Policies in Stochastic Control Systems.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2205.11991\">https://doi.org/10.48550/arXiv.2205.11991</a>.","ista":"Zikelic D, Lechner M, Chatterjee K, Henzinger TA. Learning stabilizing policies in stochastic control systems. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2205.11991\">10.48550/arXiv.2205.11991</a>.","ieee":"D. Zikelic, M. Lechner, K. Chatterjee, and T. A. Henzinger, “Learning stabilizing policies in stochastic control systems,” <i>arXiv</i>. .","ama":"Zikelic D, Lechner M, Chatterjee K, Henzinger TA. Learning stabilizing policies in stochastic control systems. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2205.11991\">10.48550/arXiv.2205.11991</a>","short":"D. Zikelic, M. Lechner, K. Chatterjee, T.A. Henzinger, ArXiv (n.d.)."},"date_created":"2023-11-24T13:22:30Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"14539"}]},"ec_funded":1}]