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Forward analysis for WSTS. III: Karp-Miller trees. (English) Zbl 07215292
Summary: This paper is a sequel of [A. Finkel and J. Goubault-Larrecq, LIPIcs – Leibniz Int. Proc. Inform. 3, 433–444 (2009; Zbl 1236.68183)] and [A. Finkel and J. Goubault-Larrecq, Log. Methods Comput. Sci. 8, No. 3, Paper No. 28, 35 p. (2012; Zbl 1248.68329)]. 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.
MSC:
03B70 Logic in computer science
68 Computer science
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