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Bideterministic Automata and Minimal Representations of Regular Languages

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Implementation and Application of Automata (CIAA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2759))

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Abstract

Bideterministic automata are deterministic automata with the property of their reversal automata also being deterministic. It has been known that a bideterministic automaton is the minimal deterministic automaton accepting its language. This paper shows that any bideterministic automaton is the unique minimal automaton among all (including nondeterministic) automata accepting the same language. We also present a more general result that shows that under certain conditions a minimal deterministic automaton accepting some language or the reversal of the minimal deterministic automaton of the reversal language is a minimal automaton representation of the language. These conditions can be checked in polynomial time.

Work supported by the Academy of Finland grant 201560.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Helsinki, P.O. Box 26, 00014, Finland

    Hellis Tamm & Esko Ukkonen

Authors
  1. Hellis Tamm
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  2. Esko Ukkonen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, 99163, USA

    Zhe Dang

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Tamm, H., Ukkonen, E. (2003). Bideterministic Automata and Minimal Representations of Regular Languages. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_7

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  • DOI: https://doi.org/10.1007/3-540-45089-0_7

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40561-0

  • Online ISBN: 978-3-540-45089-4

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