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Regular Model Checking Revisited

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Model Checking, Synthesis, and Learning

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13030))

Abstract

In this contribution we revisit regular model checking, a powerful framework—pioneered by Bengt Jonsson et al.—that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of processes). We provide a reformulation of regular model checking with length-preserving transducers in terms of existential second-order theory over automatic structures. We argue that this is a natural formulation that enables us to tap into powerful synthesis techniques that have been extensively studied in the software verification community. More precisely, in this formulation the first-order part represents the verification conditions for the desired correctness property (for which we have complete solvers), whereas the existentially quantified second-order variables represent the relations to be synthesized. We show that many interesting correctness properties can be formulated in this way, examples being safety, liveness, bisimilarity, and games. More importantly, we show that this new formulation allows new interesting benchmarks (and old regular model checking benchmarks that were previously believed to be difficult), especially in the domain of parameterized system verification, to be solved.

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Acknowledgment

First and foremost, we thank Bengt Jonsson for a source of inspiration for our research for many years, as well as for being the best colleague and friend one could wish for. We also thank our numerous collaborators in our work on regular model checking that led to this work, including Parosh Abdulla, Yu-Fang Chen, Lukas Holik, Chih-Duo Hong, Ondrej Lengal, Leonid Libkin, Rupak Majumdar, and Tomas Vojnar. This research was sponsored in part by the ERC Starting Grant 759969 (AV-SMP), Max-Planck Fellowship, the Swedish Research Council (VR) under grant 2018-04727, and by the Swedish Foundation for Strategic Research (SSF) under the project WebSec (Ref. RIT17-0011).

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Authors and Affiliations

  1. TU Kaiserslautern and MPI-SWS, Kaiserslautern, Germany

    Anthony W. Lin

  2. Uppsala University, Uppsala, Sweden

    Philipp Rümmer

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  1. Anthony W. Lin
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  2. Philipp Rümmer
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Correspondence to Anthony W. Lin or Philipp Rümmer .

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Editors and Affiliations

  1. Universität Oldenburg, Oldenburg, Germany

    Ernst-Rüdiger Olderog

  2. TU Dortmund University, Dortmund, Germany

    Bernhard Steffen

  3. Uppsala University, Uppsala, Sweden

    Wang Yi

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Lin, A.W., Rümmer, P. (2021). Regular Model Checking Revisited. In: Olderog, ER., Steffen, B., Yi, W. (eds) Model Checking, Synthesis, and Learning. Lecture Notes in Computer Science(), vol 13030. Springer, Cham. https://doi.org/10.1007/978-3-030-91384-7_6

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  • DOI: https://doi.org/10.1007/978-3-030-91384-7_6

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