Download PDFOpen PDF in browserAutomated Synthesis of Decision Lists for Polynomial Specifications over Integers19 pages•Published: May 26, 2024AbstractIn this work, we consider two sets I and O of bounded integer variables, modeling the inputs and outputs of a program. Given a specification Post, which is a Boolean combination of linear or polynomial inequalities with real coefficients over I ∪ O, our goal is to synthesize the weakest possible pre-condition Pre and a program P satisfying the Hoare triple {Pre}P{Post}. We provide a novel, practical, sound and complete algorithm, inspired by Farkas’ Lemma and Handelman’s Theorem, that synthesizes both the program P and the pre-condition Pre over a bounded integral region. Our approach is exact and guaranteed to find the weakest pre-condition. Moreover, it always synthesizes both P and Pre as linear decision lists. Thus, our output consists of simple programs and pre- conditions that facilitate further static analysis. We also provide experimental results over benchmarks showcasing the real-world applicability of our approach and considerable performance gains over the state-of-the-art.1Keyphrases: decision lists, non-linear integer arithmetic, static analysis, synthesis In: Nikolaj Bjorner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 484--502
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