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Generic Model Checking for Modal Fixpoint Logics in COOL-MC

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14499))

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Abstract

We report on COOL-MC, a model checking tool for fixpoint logics that is parametric in the branching type of models (non-deterministic, game-based, probabilistic etc.) and in the next-step modalities used in formulae. The tool implements generic model checking algorithms developed in coalgebraic logic that are easily adapted to concrete instance logics. Apart from the standard modal \(\mu \)-calculus, COOL-MC currently supports alternating-time, graded, probabilistic and monotone variants of the \(\mu \)-calculus, but is also effortlessly extensible with new instance logics. The model checking process is realized by polynomial reductions to parity game solving, or, alternatively, by a local model checking algorithm that directly computes the extensions of formulae in a lazy fashion, thereby potentially avoiding the construction of the full parity game. We evaluate COOL-MC on informative benchmark sets.

D. Hausmann—Funded by the ERC Consolidator grant D-SynMA (No. 772459).

M. Humml—Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 377333057 and 393541319/GRK2475/1-2019.

L. Schröder—Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 419850228.

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Data Availability Statement

All data to reproduce the findings in this paper are available online. The COOL-MC source code used to compile the artifact is available at tag VMCAI-2024 of the COOL git repository [9]. Pre-compiled Linux executables as well as a docker container to reproduce the measurements displayed in the figures and tables of this paper are available online [19].

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Authors and Affiliations

  1. University of Gothenburg, Gothenburg, Sweden

    Daniel Hausmann

  2. Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany

    Merlin Humml, Simon Prucker, Lutz Schröder & Aaron Strahlberger

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  1. Daniel Hausmann
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  4. Lutz Schröder
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Correspondence to Daniel Hausmann .

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Editors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Rayna Dimitrova

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

  3. New York University, New York, NY, USA

    Sebastian Wolff

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Hausmann, D., Humml, M., Prucker, S., Schröder, L., Strahlberger, A. (2024). Generic Model Checking for Modal Fixpoint Logics in COOL-MC. In: Dimitrova, R., Lahav, O., Wolff, S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2024. Lecture Notes in Computer Science, vol 14499. Springer, Cham. https://doi.org/10.1007/978-3-031-50524-9_8

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  • DOI: https://doi.org/10.1007/978-3-031-50524-9_8

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