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Complexity of Verification and Synthesis of Threshold Automata

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Automated Technology for Verification and Analysis (ATVA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12302))

Abstract

Threshold automata are a formalism for modeling and analyzing fault-tolerant distributed algorithms, recently introduced by Konnov, Veith, and Widder, describing protocols executed by a fixed but arbitrary number of processes. We conduct the first systematic study of the complexity of verification and synthesis problems for threshold automata. We prove that the coverability, reachability, safety, and liveness problems are NP-complete, and that the bounded synthesis problem is \(\varSigma _p^2\) complete. A key to our results is a novel characterization of the reachability relation of a threshold automaton as an existential Presburger formula. The characterization also leads to novel verification and synthesis algorithms. We report on an implementation, and provide experimental results.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 787367 (PaVeS).

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Notes

  1. 1.

    A full version of this paper containing additional details and proofs can be found at https://arxiv.org/abs/2007.06248.

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Authors and Affiliations

  1. Technische Universität München, Munich, Germany

    A. R. Balasubramanian, Javier Esparza & Marijana Lazić

Authors
  1. A. R. Balasubramanian
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  2. Javier Esparza
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  3. Marijana Lazić
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Correspondence to A. R. Balasubramanian .

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Editors and Affiliations

  1. Vietnam National University (VNU-UET), Hanoi, Vietnam

    Dang Van Hung

  2. University of Pennsylvania, Philadelphia, PA, USA

    Oleg Sokolsky

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Balasubramanian, A.R., Esparza, J., Lazić, M. (2020). Complexity of Verification and Synthesis of Threshold Automata. In: Hung, D.V., Sokolsky, O. (eds) Automated Technology for Verification and Analysis. ATVA 2020. Lecture Notes in Computer Science(), vol 12302. Springer, Cham. https://doi.org/10.1007/978-3-030-59152-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-59152-6_8

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