conference paper published yes Krishnendu Chatterjee author 2E5DCA20-F248-11E8-B48F-1D18A9856A870000-0002-4561-241X Hongfei Fu author Amir Goharshady author 391365CE-F248-11E8-B48F-1D18A9856A870000-0003-1702-6584 RupakMajumdar editor ViktorKunčak editor KrCh department CAV: Computer Aided Verification Game Theory project Quantitative Graph Games: Theory and Applications project 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. Springer2017Heidelberg, Germany eng 978-331963389-3 1705.00317 00043190090000310.1007/978-3-319-63390-9_3 1042741 - 63 https://research-explorer.ista.ac.at/record/7014 https://research-explorer.ista.ac.at/record/8934 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> 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> K. Chatterjee, H. Fu, A.K. Goharshady, in:, R. Majumdar, V. Kunčak (Eds.), Springer, 2017, pp. 41–63. 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>. 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>. Chatterjee K, Fu H, Goharshady AK. 2017. Non-polynomial worst case analysis of recursive programs. CAV: Computer Aided Verification, LNCS, vol. 10427, 41–63. 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. 6392018-12-11T11:47:39Z2026-04-17T22:31:21Z