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Exact Searching for the Smallest Deterministic Automaton

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12744))

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Abstract

We propose an approach to minimum-state deterministic finite automaton (DFA) inductive synthesis that is based on using satisfiability modulo theories (SMT) solvers. To that end, we explain how DFAs and their response to input samples can be encoded as logic formulas with integer variables, equations, and uninterpreted functions. An SMT solver is then tasked with finding an assignment for such a formula, from which we can extract the automaton of a required size. We provide an implementation of this approach, which we use to conduct experiments on a series of benchmarks. The results showed that our method outperforms in terms of CPU time other SAT and SMT approaches and other exact algorithms on prepared benchmarks.

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Notes

  1. 1.

    https://github.com/wieczorekw/wieczorekw.github.io/tree/master/SMT4DFA.

  2. 2.

    https://github.com/Z3Prover/z3.

  3. 3.

    The independent set problem and the well-known clique problem are complementary: a clique in G is an independent set in the complement graph of G and vice versa.

  4. 4.

    https://github.com/wieczorekw/wieczorekw.github.io/tree/master/SMT4DFA.

  5. 5.

    We have obtained Linux executable file from the authors.

  6. 6.

    https://github.com/lazarow/exbar.

  7. 7.

    https://github.com/ctlab/DFA-Inductor.

  8. 8.

    https://gitlab.science.ru.nl/rick/z3gi/tree/lata.

  9. 9.

    Refer to Chap. 6 of [11] for the formal definition of this concept.

  10. 10.

    https://github.com/lazarow/exbar/tree/master/samples.

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Authors and Affiliations

  1. University of Bielsko-Biala, Willowa 2, 43-309, Bielsko-Biala, Poland

    Wojciech Wieczorek

  2. University of Silesia in Katowice, Bankowa 14, 40-007, Katowice, Poland

    Łukasz Strąk & Arkadiusz Nowakowski

  3. Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland

    Olgierd Unold

Authors
  1. Wojciech Wieczorek
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  2. Łukasz Strąk
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  3. Arkadiusz Nowakowski
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  4. Olgierd Unold
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Corresponding author

Correspondence to Łukasz Strąk .

Editor information

Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M.A. Sloot

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Wieczorek, W., Strąk, Ł., Nowakowski, A., Unold, O. (2021). Exact Searching for the Smallest Deterministic Automaton. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12744. Springer, Cham. https://doi.org/10.1007/978-3-030-77967-2_5

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  • DOI: https://doi.org/10.1007/978-3-030-77967-2_5

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