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On existentially first-order definable languages and their relation to NP

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Automata, Languages and Programming (ICALP 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1443))

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Abstract

Under the assumption that the Polynomial-Time Hierarchy does not collapse we show that a regular language L determines NP as an unbalanced polynomial-time leaf language if and only if L is existentially but not quantifierfree definable in FO[<, min, max, −1, +1]. The proof relies on the result of Pin & Weil [PVV97] characterizing the automata of existentially first-order definable languages.

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Author information

Authors and Affiliations

  1. Universität Heidelberg, Deutschland

    Bernd Borchert & Frank Stephan

  2. Technische Universität Dresden, Deutschland

    Dietrich Kuske

Authors
  1. Bernd Borchert
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  2. Dietrich Kuske
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  3. Frank Stephan
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Editor information

Kim G. Larsen Sven Skyum Glynn Winskel

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© 1998 Springer-Verlag Berlin Heidelberg

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Borchert, B., Kuske, D., Stephan, F. (1998). On existentially first-order definable languages and their relation to NP. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055037

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  • DOI: https://doi.org/10.1007/BFb0055037

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64781-2

  • Online ISBN: 978-3-540-68681-1

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