{"date_updated":"2024-03-25T23:30:18Z","publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.00317"}],"month":"10","day":"01","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7014","ec_funded":1,"language":[{"iso":"eng"}],"isi":1,"article_number":"20","scopus_import":"1","issue":"4","status":"public","project":[{"grant_number":"ICT15-003","name":"Efficient Algorithms for Computer Aided Verification","_id":"25892FC0-B435-11E9-9278-68D0E5697425"},{"grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","_id":"25832EC2-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307"},{"_id":"267066CE-B435-11E9-9278-68D0E5697425","name":"Quantitative Analysis of Probablistic Systems with a focus on Crypto-currencies"},{"name":"Quantitative Game-theoretic Analysis of Blockchain Applications and Smart Contracts","_id":"266EEEC0-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","related_material":{"record":[{"status":"public","id":"639","relation":"earlier_version"},{"id":"8934","status":"public","relation":"dissertation_contains"}]},"type":"journal_article","publication":"ACM Transactions on Programming Languages and Systems","date_published":"2019-10-01T00:00:00Z","citation":{"short":"K. Chatterjee, H. Fu, A.K. Goharshady, ACM Transactions on Programming Languages and Systems 41 (2019).","ieee":"K. Chatterjee, H. Fu, and A. K. Goharshady, “Non-polynomial worst-case analysis of recursive programs,” <i>ACM Transactions on Programming Languages and Systems</i>, vol. 41, no. 4. ACM, 2019.","mla":"Chatterjee, Krishnendu, et al. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” <i>ACM Transactions on Programming Languages and Systems</i>, vol. 41, no. 4, 20, ACM, 2019, doi:<a href=\"https://doi.org/10.1145/3339984\">10.1145/3339984</a>.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Non-Polynomial Worst-Case Analysis of Recursive Programs.” <i>ACM Transactions on Programming Languages and Systems</i>. ACM, 2019. <a href=\"https://doi.org/10.1145/3339984\">https://doi.org/10.1145/3339984</a>.","ista":"Chatterjee K, Fu H, Goharshady AK. 2019. Non-polynomial worst-case analysis of recursive programs. ACM Transactions on Programming Languages and Systems. 41(4), 20.","ama":"Chatterjee K, Fu H, Goharshady AK. Non-polynomial worst-case analysis of recursive programs. <i>ACM Transactions on Programming Languages and Systems</i>. 2019;41(4). doi:<a href=\"https://doi.org/10.1145/3339984\">10.1145/3339984</a>","apa":"Chatterjee, K., Fu, H., &#38; Goharshady, A. K. (2019). Non-polynomial worst-case analysis of recursive programs. <i>ACM Transactions on Programming Languages and Systems</i>. ACM. <a href=\"https://doi.org/10.1145/3339984\">https://doi.org/10.1145/3339984</a>"},"volume":41,"year":"2019","publisher":"ACM","intvolume":"        41","author":[{"last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu"},{"full_name":"Fu, Hongfei","last_name":"Fu","first_name":"Hongfei"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","first_name":"Amir Kafshdar","last_name":"Goharshady","full_name":"Goharshady, Amir Kafshdar","orcid":"0000-0003-1702-6584"}],"date_created":"2019-11-13T08:33:43Z","abstract":[{"lang":"eng","text":"We study the problem of developing efficient approaches for proving\r\nworst-case bounds of non-deterministic recursive programs. Ranking functions\r\nare sound and complete for proving termination and worst-case bounds of\r\nnonrecursive programs. First, we apply ranking functions to recursion,\r\nresulting in measure functions. We show that measure functions provide a sound\r\nand complete approach to prove worst-case bounds of non-deterministic recursive\r\nprograms. Our second contribution is the synthesis of measure functions in\r\nnonpolynomial forms. We show that non-polynomial measure functions with\r\nlogarithm and exponentiation can be synthesized through abstraction of\r\nlogarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem\r\nusing linear programming. While previous methods obtain worst-case polynomial\r\nbounds, our approach can synthesize bounds of the form $\\mathcal{O}(n\\log n)$\r\nas well as $\\mathcal{O}(n^r)$ where $r$ is not an integer. We present\r\nexperimental results to demonstrate that our approach can obtain efficiently\r\nworst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the\r\ndivide-and-conquer algorithm for the Closest-Pair problem, where we obtain\r\n$\\mathcal{O}(n \\log n)$ worst-case bound, and (ii) Karatsuba's algorithm for\r\npolynomial multiplication and Strassen's algorithm for matrix multiplication,\r\nwhere we obtain $\\mathcal{O}(n^r)$ bound such that $r$ is not an integer and\r\nclose to the best-known bounds for the respective algorithms."}],"oa":1,"title":"Non-polynomial worst-case analysis of recursive programs","doi":"10.1145/3339984","article_type":"original","external_id":{"isi":["000564108400001"],"arxiv":["1705.00317"]},"article_processing_charge":"No","department":[{"_id":"KrCh"}]}