License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2022.23
URN: urn:nbn:de:0030-drops-170862
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17086/
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Esparza, Javier ; Raskin, Mikhail ; Welzel, Christoph

Regular Model Checking Upside-Down: An Invariant-Based Approach

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Abstract

Regular model checking is a technique for the verification of infinite-state systems whose configurations can be represented as finite words over a suitable alphabet. It applies to systems whose set of initial configurations is regular, and whose transition relation is captured by a length-preserving transducer. To verify safety properties, regular model checking iteratively computes automata recognizing increasingly larger regular sets of reachable configurations, and checks if they contain unsafe configurations. Since this procedure often does not terminate, acceleration, abstraction, and widening techniques have been developed to compute a regular superset of the reachable configurations.
In this paper we develop a complementary procedure. Instead of approaching the set of reachable configurations from below, we start with the set of all configurations and approach it from above. We use that the set of reachable configurations is equal to the intersection of all inductive invariants of the system. Since this intersection is non-regular in general, we introduce b-bounded invariants, defined as those representable by CNF-formulas with at most b clauses. We prove that, for every b ≥ 0, the intersection of all b-bounded inductive invariants is regular, and we construct an automaton recognizing it. We show that whether this automaton accepts some unsafe configuration is in EXPSPACE for every b ≥ 0, and PSPACE-complete for b = 1. Finally, we study how large must b be to prove safety properties of a number of benchmarks.

BibTeX - Entry

@InProceedings{esparza_et_al:LIPIcs.CONCUR.2022.23,
  author =	{Esparza, Javier and Raskin, Mikhail and Welzel, Christoph},
  title =	{{Regular Model Checking Upside-Down: An Invariant-Based Approach}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17086},
  URN =		{urn:nbn:de:0030-drops-170862},
  doi =		{10.4230/LIPIcs.CONCUR.2022.23},
  annote =	{Keywords: parameterized verification, structural analysis, regular languages, regular model-checking, traps}
}

Keywords: parameterized verification, structural analysis, regular languages, regular model-checking, traps
Collection: 33rd International Conference on Concurrency Theory (CONCUR 2022)
Issue Date: 2022
Date of publication: 06.09.2022
Supplementary Material: Software (Repository of examples): https://doi.org/10.5281/zenodo.6483615

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