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On the Transformation of Two-Way Deterministic Finite Automata to Unambiguous Finite Automata

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Book cover Language and Automata Theory and Applications (LATA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12638))

Abstract

The paper estimates the number of states in an unambiguous finite automaton (UFA) that is sufficient and in the worst case necessary to simulate an n-state two-way deterministic finite automaton (2DFA). It is proved that a 2DFA with n states can be transformed to a UFA with fewer than \(2^n \cdot n!\) states. On the other hand, for every n, there is a language recognized by an n-state 2DFA that requires a UFA with at least \(\varOmega ((4\sqrt{2})^n \cdot n^{-1/2})\) states. The latter result is proved by estimating the rank of a certain matrix.

Research supported by Russian Science Foundation, project 18-11-00100.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, St. Petersburg State University, 7/9 Universitetskaya nab., Saint Petersburg, 199034, Russia

    Semyon Petrov & Alexander Okhotin

Authors
  1. Semyon Petrov
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  2. Alexander Okhotin
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Correspondence to Alexander Okhotin .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Alberto Leporati

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. Ariel University, Ariel, Israel

    Dana Shapira

  4. University of Milano-Bicocca, Milan, Italy

    Claudio Zandron

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Petrov, S., Okhotin, A. (2021). On the Transformation of Two-Way Deterministic Finite Automata to Unambiguous Finite Automata. In: Leporati, A., Martín-Vide, C., Shapira, D., Zandron, C. (eds) Language and Automata Theory and Applications. LATA 2021. Lecture Notes in Computer Science(), vol 12638. Springer, Cham. https://doi.org/10.1007/978-3-030-68195-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-68195-1_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68194-4

  • Online ISBN: 978-3-030-68195-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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