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Using Sat Solvers for Synchronization Issues in Partial Deterministic Automata

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Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1090))

Abstract

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used.

Supported by the Ministry of Science and Higher Education of the Russian Federation, projects no. 1.580.2016 and 1.3253.2017, and the Competitiveness Enhancement Program of Ural Federal University.

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Notes

  1. 1.

    The conventional concept of an NFA includes distinguishing two non-empty subsets of Q consisting of initial and final states. As these play no role in our considerations, the above simplified definition well suffices for the purpose of this paper.

  2. 2.

    We refer the reader to [4, Chapters 3 and 10] for a detailed account of profound connections between codes and automata.

  3. 3.

    We refer the reader to the survey [10] or to the handbook [6] for a detailed discussion of the approach and examples of its successful applications in various areas.

  4. 4.

    In principle, it may happen that we never reach such an instance (which indicates that either \(\mathscr {A}\) is not carefully synchronizing or the minimum length of carefully synchronizing words for \(\mathscr {A}\) is too big so that MiniSat cannot handle the resulting SAT instance) but we have not observed such “bad” cases in our experiments with randomly generated PFAs.

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Acknowledgements

The authors are very much indebted to the referees for their valuable remarks.

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Authors and Affiliations

  1. Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt

    Hanan Shabana

  2. Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia

    Hanan Shabana & Mikhail V. Volkov

Authors
  1. Hanan Shabana
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  2. Mikhail V. Volkov
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Correspondence to Mikhail V. Volkov .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Igor Bykadorov

  2. University of Greenwich, London, UK

    Vitaly Strusevich

  3. University of Aveiro, Aveiro, Portugal

    Tatiana Tchemisova

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Shabana, H., Volkov, M.V. (2019). Using Sat Solvers for Synchronization Issues in Partial Deterministic Automata. In: Bykadorov, I., Strusevich, V., Tchemisova, T. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Communications in Computer and Information Science, vol 1090. Springer, Cham. https://doi.org/10.1007/978-3-030-33394-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-33394-2_9

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