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On Existentially First-Order Definable Languages and Their Relation to NP

Published online by Cambridge University Press:  15 August 2002

Bernd Borchert ,
Dietrich Kuske  and
Frank Stephan
Bernd Borchert
Affiliation:
Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
Dietrich Kuske
Affiliation:
Institut für Algebra, Technische Universität Dresden, 01062 Dresden, Germany
Frank Stephan
Affiliation:
Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany
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Abstract

Under the assumption that the Polynomial-Time Hierarchy does not collapse we show for a regular language L: the unbalanced polynomial-time leaf language class determined by L equals  iff L is existentially but not quantifierfree definable in FO[<, min, max, +1, −1]. Furthermore, no such class lies properly between NP and co-1-NP or NP⊕co-NP. The proofs rely on a result of Pin and Weil characterizing the automata of existentially first-order definable languages.

Keywords

Leaf languagesNPfirst-order definable languages.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 3 , May 1999 , pp. 259 - 269
Copyright
© EDP Sciences, 1999

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