[{"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1705.00317"}],"oa":1,"volume":10427,"arxiv":1,"article_processing_charge":"No","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."}],"_id":"639","date_published":"2017-01-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-06-02T08:53:47Z","scopus_import":1,"external_id":{"arxiv":["1705.00317"]},"publication_identifier":{"isbn":["978-331963389-3"]},"editor":[{"last_name":"Majumdar","full_name":"Majumdar, Rupak","first_name":"Rupak"},{"first_name":"Viktor","full_name":"Kunčak, Viktor","last_name":"Kunčak"}],"publist_id":"7149","year":"2017","oa_version":"Submitted Version","publisher":"Springer","quality_controlled":"1","department":[{"_id":"KrCh"}],"intvolume":"     10427","status":"public","page":"41 - 63","month":"01","date_created":"2018-12-11T11:47:39Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"8934"},{"id":"7014","relation":"later_version","status":"public"}]},"project":[{"name":"Game Theory","grant_number":"S11407","call_identifier":"FWF","_id":"25863FF4-B435-11E9-9278-68D0E5697425"},{"grant_number":"279307","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7","_id":"2581B60A-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"doi":"10.1007/978-3-319-63390-9_3","ec_funded":1,"citation":{"short":"K. Chatterjee, H. Fu, A.K. Goharshady, in:, R. Majumdar, V. Kunčak (Eds.), Springer, 2017, pp. 41–63.","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>","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>","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>.","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.","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.","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>."},"conference":{"end_date":"2017-07-28","start_date":"2017-07-24","name":"CAV: Computer Aided Verification","location":"Heidelberg, Germany"},"title":"Non-polynomial worst case analysis of recursive programs","day":"01","alternative_title":["LNCS"],"type":"conference","author":[{"first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"last_name":"Fu","full_name":"Fu, Hongfei","first_name":"Hongfei"},{"first_name":"Amir","full_name":"Goharshady, Amir","last_name":"Goharshady","id":"391365CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1702-6584"}]}]