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arXiv · 1710.07258

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

Michael Blondin·Alain Finkel·Jean Goubault-Larrecq
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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.

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Michael Blondin, Alain Finkel, Jean Goubault-Larrecq. 2017-10-19. Forward Analysis for WSTS, Part III: Karp-Miller Trees. https://doi.org/10.23638/lmcs-16(2%3A13)2020

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