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Finding All Minimum-Size DFA Consistent with Given Examples: SAT-Based Approach

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Software Engineering and Formal Methods (SEFM 2017)

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Abstract

Deterministic finite automaton (DFA) is a fundamental concept in the theory of computation. The NP-hard DFA identification problem can be efficiently solved by translation to the Boolean satisfiability problem (SAT). Previously we developed a technique to reduce the problem search space by enforcing DFA states to be enumerated in breadth-first search (BFS) order. We proposed symmetry breaking predicates, which can be added to Boolean formulae representing various automata identification problems. In this paper we continue the study of SAT-based approaches. First, we propose new predicates based on depth-first search order. Second, we present three methods to identify all non-isomorphic automata of the minimum size instead of just one—the P-complete problem which has not been solved before. Third, we revisited our implementation of the BFS-based approach and conducted new evaluation experiments. It occurs that BFS-based approach outperforms all other exact algorithms for DFA identification and can be effectively applied for finding all solutions of the problem.

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Notes

  1. 1.

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

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Acknowledgements

The authors would like to thank Igor Buzhinsky, Daniil Chivilikhin, Maxim Buzdalov for useful comments. This work was financially supported by the Government of Russian Federation, Grant 074-U01.

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Correspondence to Ilya Zakirzyanov .

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Zakirzyanov, I., Shalyto, A., Ulyantsev, V. (2018). Finding All Minimum-Size DFA Consistent with Given Examples: SAT-Based Approach. In: Cerone, A., Roveri, M. (eds) Software Engineering and Formal Methods. SEFM 2017. Lecture Notes in Computer Science(), vol 10729. Springer, Cham. https://doi.org/10.1007/978-3-319-74781-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-74781-1_9

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