[{"arxiv":1,"publist_id":"7149","publication_identifier":{"isbn":["978-331963389-3"]},"related_material":{"record":[{"relation":"later_version","id":"7014","status":"public"},{"id":"8934","status":"public","relation":"dissertation_contains"}]},"month":"01","title":"Non-polynomial worst case analysis of recursive programs","volume":10427,"abstract":[{"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.","lang":"eng"}],"type":"conference","fulldoi":"https://doi.org/10.1007/978-3-319-63390-9_3","project":[{"grant_number":"S11407","name":"Game Theory","_id":"25863FF4-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"}],"author":[{"last_name":"Chatterjee","orcid":"0000-0002-4561-241X","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Fu","full_name":"Fu, Hongfei","first_name":"Hongfei"},{"id":"391365CE-F248-11E8-B48F-1D18A9856A87","first_name":"Amir","orcid":"0000-0003-1702-6584","full_name":"Goharshady, Amir","last_name":"Goharshady"}],"date_created":"2018-12-11T11:47:39Z","department":[{"_id":"KrCh"}],"intvolume":"     10427","date_updated":"2026-11-11T23:30:55Z","page":"41 - 63","publisher":"Springer","main_file_link":[{"url":"https://arxiv.org/abs/1705.00317","open_access":"1"}],"doi":"10.1007/978-3-319-63390-9_3","isi":1,"publication_status":"published","external_id":{"isi":["000431900900003"],"arxiv":["1705.00317"]},"conference":{"end_date":"2017-07-28","start_date":"2017-07-24","location":"Heidelberg, Germany","name":"CAV: Computer Aided Verification"},"ec_funded":1,"alternative_title":["LNCS"],"editor":[{"first_name":"Rupak","full_name":"Majumdar, Rupak","last_name":"Majumdar"},{"full_name":"Kunčak, Viktor","first_name":"Viktor","last_name":"Kunčak"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","scopus_import":"1","quality_controlled":"1","status":"public","_id":"639","citation":{"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.","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>","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>","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>.","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."},"year":"2017","date_published":"2017-01-01T00:00:00Z","language":[{"iso":"eng"}],"oa":1,"oa_version":"Submitted Version","article_processing_charge":"No"}]