Forward Analysis for WSTS, Part III: Karp-Miller Trees

Michael Blondin, A. Finkel, J. Goubault-Larrecq
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引用次数: 7

Abstract

This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433-444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downward-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural effectiveness assumptions, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.
WSTS的正向分析,第三部分:Karp-Miller树
本文是“WSTS的正向分析,第一部分:完井”[STACS 2009, LZI Intl.]的续作。“WSTS的前向分析,Part II: Complete WSTS”[j].计算机科学学报,33(3),2012。在这两篇论文中,我们提供了一个框架,使用向下封闭集的有限表示来进行WSTS的前向可达性分析。我们进一步发展了这个框架,得到了一类新的非常wsts的通用Karp-Miller算法。这使我们能够证明非常wsts的可覆盖性集可以计算为它们的有限理想分解。在自然有效性假设下,我们还证明了LTL模型对非常wsts的检查是可确定的。我们的过程的终止取决于我们研究的加速度水平的新概念。我们根据序数来描述那些只允许有限多个加速度的域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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