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Proving the Existence of Fair Paths in Infinite-State Systems

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12597))

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Abstract

In finite-state systems, true existential properties admit witnesses in form of lasso-shaped fair paths. When dealing with the infinite-state case (e.g. software non-termination, model checking of hybrid automata) this is no longer the case. In this paper, we propose a compositional approach for proving the existence of fair paths of infinite-state systems. First, we describe a formal approach to prove the existence of a non-empty under-approximation of the original system that only contains fair paths. Second, we define an automated procedure that, given a set of hints (in form of basic components), searches for a suitable composition proving the existence of a fair path. We experimentally evaluate the approach on examples taken from both software and hybrid systems, showing its wide applicability and expressiveness.

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Notes

  1. 1.

    The extended version is available at https://enricomagnago.com/proving_the_existence_of_fair_paths_in_infinite-state_systems_extended.pdf.

  2. 2.

    Hence, \(S^M \subseteq \bigcup _{j} S^j\) and \(\forall j \not = k : S^j \cap S^k = \emptyset \)

  3. 3.

    Note that this is the liveness-to-safety construction of [7].

  4. 4.

    Artifact DOI: https://doi.org/10.5281/zenodo.4271411.

  5. 5.

    This allows the procedure to make progress even if the solver is unable to provide a definite answer for some query. Many of the benchmarks require reasoning in mixed integer/real non-linear arithmetic (in general undecidable).

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  1. Fondazione Bruno Kessler, Trento, Italy

    Alessandro Cimatti, Alberto Griggio & Enrico Magnago

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  1. Alessandro Cimatti
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  2. Alberto Griggio
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Correspondence to Enrico Magnago .

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  1. University of Copenhagen, Copenhagen, Denmark

    Fritz Henglein

  2. Tel Aviv University, Tel Aviv, Israel

    Sharon Shoham

  3. Technion, Haifa, Israel

    Yakir Vizel

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Cimatti, A., Griggio, A., Magnago, E. (2021). Proving the Existence of Fair Paths in Infinite-State Systems. In: Henglein, F., Shoham, S., Vizel, Y. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2021. Lecture Notes in Computer Science(), vol 12597. Springer, Cham. https://doi.org/10.1007/978-3-030-67067-2_6

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