@inproceedings{1bfec356c6a749928639661467b5b162,
title = "Breaking the Mold: Nonlinear Ranking Function Synthesis Without Templates",
abstract = "This paper studies the problem of synthesizing (lexicographic) polynomial ranking functions for loops that can be described in polynomial arithmetic over integers and reals. While the analogous ranking function synthesis problem for linear arithmetic is decidable, even checking whether a given function ranks an integer loop is undecidable in the nonlinear setting. We side-step the decidability barrier by working within the theory of linear integer/real rings (LIRR) rather than the standard model of arithmetic. We develop a termination analysis that is guaranteed to succeed if a loop (expressed as a formula) admits a (lexicographic) polynomial ranking function. In contrast to template-based ranking function synthesis in real arithmetic, our completeness result holds for lexicographic ranking functions of unbounded dimension and degree, and effectively subsumes linear lexicographic ranking function synthesis for linear integer loops.",
keywords = "lexicographic ranking functions, monotone, nonlinear arithmetic, polynomial ranking functions, ranking functions, termination",
author = "Shaowei Zhu and Zachary Kincaid",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.; 36th International Conference on Computer Aided Verification, CAV 2024 ; Conference date: 24-07-2024 Through 27-07-2024",
year = "2024",
doi = "10.1007/978-3-031-65627-9_21",
language = "English (US)",
isbn = "9783031656262",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "431--452",
editor = "Arie Gurfinkel and Vijay Ganesh",
booktitle = "Computer Aided Verification - 36th International Conference, CAV 2024, Proceedings",
address = "Germany",
}