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Shortest Characteristic Factors of a Deterministic Finite Automaton and Computing Its Positive Position Run by Pattern Set Matching

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SOFSEM 2024: Theory and Practice of Computer Science (SOFSEM 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14519))

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Abstract

Given a deterministic finite automaton (DFA) A, we present a simple algorithm for constructing four deterministic finite automata that accept the shortest forbidden factors, the shortest forbidden suffixes, the shortest allowed suffixes, and the shortest forbidden prefixes. We refer to these automata as the shortest characteristic factors of automaton A. If the given automaton is local, and therefore the language it accepts is strictly locally testable, the sets of its shortest characteristic factors are finite, and these four automata are acyclic. This approach simplifies existing methods for the extraction of forbidden factors and also generalizes it for all classes of input DFAs. Furthermore, we demonstrate that this type of extraction can be used for a sublinear run of an automaton for certain inputs. We define a positive position run of a deterministic finite automaton, representing all positions in an input string where the automaton reaches a final state. Finally, we present an algorithm for computing the positive position run of the automaton, which utilizes pattern set matching of its shortest forbidden factors and its shortest allowed suffixes, provided that the sets are finite. We showcase the computation of the positive position run of a local automaton using backward pattern matching, which can achieve sublinear time.

The authors acknowledge the support of the OP VVV MEYS funded project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”.

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Authors and Affiliations

  1. Faculty of Information Technology, Czech Technical University in Prague, Prague, Czech Republic

    Jan Janoušek & Štěpán Plachý

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  1. Jan Janoušek
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  2. Štěpán Plachý
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Correspondence to Štěpán Plachý .

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Editors and Affiliations

  1. University of Trier, Trier, Germany

    Henning Fernau

  2. UNSW Sydney, Sydney, NSW, Australia

    Serge Gaspers

  3. CNRS and University of Bordeaux, Talence, France

    Ralf Klasing

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Janoušek, J., Plachý, Š. (2024). Shortest Characteristic Factors of a Deterministic Finite Automaton and Computing Its Positive Position Run by Pattern Set Matching. In: Fernau, H., Gaspers, S., Klasing, R. (eds) SOFSEM 2024: Theory and Practice of Computer Science. SOFSEM 2024. Lecture Notes in Computer Science, vol 14519. Springer, Cham. https://doi.org/10.1007/978-3-031-52113-3_23

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  • DOI: https://doi.org/10.1007/978-3-031-52113-3_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-52112-6

  • Online ISBN: 978-3-031-52113-3

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