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Computing Linear Arithmetic Representation of Reachability Relation of One-Counter Automata

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Dependable Software Engineering. Theories, Tools, and Applications (SETTA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12153))

Abstract

One-counter automata (OCA) are a well-studied automata model that extends finite-state automata with one counter. The reachability problem of OCA was shown to be NP-complete when the integers in the OCA are encoded in binary. In this paper, we study the problem of computing the reachability relation of OCA. We show that, for each OCA, an existential Presburger arithmetic (EPA) formula of polynomial size can be computed in polynomial time to represent its reachability relation. This yields a polynomial-time reduction from the reachability problem of OCA to the satisfiability problem of EPA, enabling its solution via off-the-shelf SMT solvers. We implement the algorithm and provide the first tool OCAReach for the reachability problem of OCA. The experimental results demonstrate the efficacy of our approach.

This work is supported by Guangdong Science and Technology Department grant (No. 2018B010107004), Overseas Grant (KFKT2018A16) from the State Key Laboratory of Novel Software Technology, Nanjing University, China, the NSFC grants (No. 61872340), Natural Science Foundation of Guangdong Province, China (No. 2019A1515011689), the Open Project of Shanghai Key Laboratory of Trustworthy Computing (No. 07dz22304201601), and the INRIA-CAS joint research project VIP.

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Notes

  1. 1.

    Available at https://github.com/SpencerL-Y/OCAReach.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Xie Li, Zhilin Wu & Mingji Xia

  2. Department of Computer Science, University of Surrey, Guildford, UK

    Taolue Chen

  3. University of Chinese Academy of Sciences, Beijing, China

    Xie Li

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  1. Xie Li
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Correspondence to Zhilin Wu .

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  1. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Jun Pang

  2. Chinese Academy of Sciences, Beijing, China

    Lijun Zhang

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Li, X., Chen, T., Wu, Z., Xia, M. (2020). Computing Linear Arithmetic Representation of Reachability Relation of One-Counter Automata. In: Pang, J., Zhang, L. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2020. Lecture Notes in Computer Science(), vol 12153. Springer, Cham. https://doi.org/10.1007/978-3-030-62822-2_6

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  • DOI: https://doi.org/10.1007/978-3-030-62822-2_6

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