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Computing Inductive Invariants of Regular Abstraction Frameworks

Authors Philipp Czerner , Javier Esparza , Valentin Krasotin , Christoph Welzel-Mohr

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Philipp Czerner
  • Technical University of Munich, Germany
Javier Esparza
  • Technical University of Munich, Germany
Valentin Krasotin
  • Technical University of Munich, Germany
Christoph Welzel-Mohr
  • Technical University of Munich, Germany

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Philipp Czerner, Javier Esparza, Valentin Krasotin, and Christoph Welzel-Mohr. Computing Inductive Invariants of Regular Abstraction Frameworks. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CONCUR.2024.19

Abstract

Regular transition systems (RTS) are a popular formalism for modeling infinite-state systems in general, and parameterised systems in particular. In a CONCUR 22 paper, Esparza et al. introduce a novel approach to the verification of RTS, based on inductive invariants. The approach computes the intersection of all inductive invariants of a given RTS that can be expressed as CNF formulas with a bounded number of clauses, and uses it to construct an automaton recognising an overapproximation of the reachable configurations. The paper shows that the problem of deciding if the language of this automaton intersects a given regular set of unsafe configurations is in EXPSPACE and PSPACE-hard. We introduce regular abstraction frameworks, a generalisation of the approach of Esparza et al., very similar to the regular abstractions of Hong and Lin. A framework consists of a regular language of constraints, and a transducer, called the interpretation, that assigns to each constraint the set of configurations of the RTS satisfying it. Examples of regular abstraction frameworks include the formulas of Esparza et al., octagons, bounded difference matrices, and views. We show that the generalisation of the decision problem above to regular abstraction frameworks remains in EXPSPACE, and prove a matching (non-trivial) EXPSPACE-hardness bound. EXPSPACE-hardness implies that, in the worst case, the automaton recognising the overapproximation of the reachable configurations has a double-exponential number of states. We introduce a learning algorithm that computes this automaton in a lazy manner, stopping whenever the current hypothesis is already strong enough to prove safety. We report on an implementation and show that our experimental results improve on those of Esparza et al.

Subject Classification

ACM Subject Classification
  • Theory of computation → Regular languages
  • Theory of computation → Problems, reductions and completeness
  • Theory of computation → Verification by model checking
Keywords
  • Regular model checking
  • abstraction
  • inductive invariants

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