{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of non-recursive programs. First, we apply ranking functions to recursion, resulting in measure functions, and show that they provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in non-polynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas’ Lemma, and Handelman’s Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form O(n log n) as well as O(nr) where r is not an integer. We present experimental results to demonstrate that our approach can efficiently obtain worst-case bounds of classical recursive algorithms such as Merge-Sort, Closest-Pair, Karatsuba’s algorithm and Strassen’s algorithm."}],"type":"conference","department":[{"_id":"KrCh"}],"external_id":{"arxiv":["1705.00317"]},"main_file_link":[{"url":"https://arxiv.org/abs/1705.00317","open_access":"1"}],"oa":1,"status":"public","date_published":"2017-01-01T00:00:00Z","ec_funded":1,"arxiv":1,"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"full_name":"Fu, Hongfei","first_name":"Hongfei","last_name":"Fu"},{"orcid":"0000-0003-1702-6584","last_name":"Goharshady","id":"391365CE-F248-11E8-B48F-1D18A9856A87","full_name":"Goharshady, Amir","first_name":"Amir"}],"year":"2017","project":[{"call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425","name":"Game Theory","grant_number":"S11407"},{"grant_number":"279307","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications"}],"day":"01","title":"Non-polynomial worst case analysis of recursive programs","month":"01","date_created":"2018-12-11T11:47:39Z","publist_id":"7149","page":"41 - 63","volume":10427,"date_updated":"2025-01-12T23:31:48Z","publication_status":"published","quality_controlled":"1","citation":{"ama":"Chatterjee K, Fu H, Goharshady AK. Non-polynomial worst case analysis of recursive programs. In: Majumdar R, Kunčak V, eds. Vol 10427. Springer; 2017:41-63. doi:<a href=\"https://doi.org/10.1007/978-3-319-63390-9_3\">10.1007/978-3-319-63390-9_3</a>","ieee":"K. Chatterjee, H. Fu, and A. K. Goharshady, “Non-polynomial worst case analysis of recursive programs,” presented at the CAV: Computer Aided Verification, Heidelberg, Germany, 2017, vol. 10427, pp. 41–63.","apa":"Chatterjee, K., Fu, H., &#38; Goharshady, A. K. (2017). Non-polynomial worst case analysis of recursive programs. In R. Majumdar &#38; V. Kunčak (Eds.) (Vol. 10427, pp. 41–63). Presented at the CAV: Computer Aided Verification, Heidelberg, Germany: Springer. <a href=\"https://doi.org/10.1007/978-3-319-63390-9_3\">https://doi.org/10.1007/978-3-319-63390-9_3</a>","short":"K. Chatterjee, H. Fu, A.K. Goharshady, in:, R. Majumdar, V. Kunčak (Eds.), Springer, 2017, pp. 41–63.","chicago":"Chatterjee, Krishnendu, Hongfei Fu, and Amir Kafshdar Goharshady. “Non-Polynomial Worst Case Analysis of Recursive Programs.” edited by Rupak Majumdar and Viktor Kunčak, 10427:41–63. Springer, 2017. <a href=\"https://doi.org/10.1007/978-3-319-63390-9_3\">https://doi.org/10.1007/978-3-319-63390-9_3</a>.","mla":"Chatterjee, Krishnendu, et al. <i>Non-Polynomial Worst Case Analysis of Recursive Programs</i>. Edited by Rupak Majumdar and Viktor Kunčak, vol. 10427, Springer, 2017, pp. 41–63, doi:<a href=\"https://doi.org/10.1007/978-3-319-63390-9_3\">10.1007/978-3-319-63390-9_3</a>.","ista":"Chatterjee K, Fu H, Goharshady AK. 2017. Non-polynomial worst case analysis of recursive programs. CAV: Computer Aided Verification, LNCS, vol. 10427, 41–63."},"editor":[{"last_name":"Majumdar","full_name":"Majumdar, Rupak","first_name":"Rupak"},{"last_name":"Kunčak","full_name":"Kunčak, Viktor","first_name":"Viktor"}],"oa_version":"Submitted Version","intvolume":"     10427","doi":"10.1007/978-3-319-63390-9_3","publisher":"Springer","scopus_import":1,"related_material":{"record":[{"relation":"later_version","id":"7014","status":"public"},{"status":"public","relation":"dissertation_contains","id":"8934"}]},"publication_identifier":{"isbn":["978-331963389-3"]},"article_processing_charge":"No","language":[{"iso":"eng"}],"alternative_title":["LNCS"],"conference":{"location":"Heidelberg, Germany","end_date":"2017-07-28","name":"CAV: Computer Aided Verification","start_date":"2017-07-24"},"_id":"639"}