--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Krishnendu foaf_name: Chatterjee, Krishnendu foaf_surname: Chatterjee foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-4561-241X - foaf_Person: foaf_givenName: Hongfei foaf_name: Fu, Hongfei foaf_surname: Fu - foaf_Person: foaf_givenName: Amir foaf_name: Goharshady, Amir foaf_surname: Goharshady foaf_workInfoHomepage: http://www.librecat.org/personId=391365CE-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0003-1702-6584 bibo_doi: 10.1007/978-3-319-63390-9_3 bibo_volume: 10427 dct_date: 2017^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/978-331963389-3 dct_language: eng dct_publisher: Springer@ dct_title: Non-polynomial worst case analysis of recursive programs@ ...