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first-order definable languages.

RAIRO - Theoretical Informatics and Applications (1)

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On Existentially First-Order Definable Languages and Their Relation to NP
Bernd Borchert, Dietrich Kuske, Frank Stephan
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 33 / Issue 3 / May 1999

Published online by Cambridge University Press:

15 August 2002, pp. 259-269

Print publication:

May 1999
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Under the assumption that the Polynomial-TimeHierarchy does not collapsewe show for a regular language L:the unbalanced polynomial-time leaf language class determined by L equals iff L is existentially but notquantifierfree definable in FO[<, min, max, +1, −1].Furthermore, no suchclass lies properly between NP and co-1-NP or NP⊕co-NP. The proofs rely on a result of Pin and Weilcharacterizing the automata of existentially first-order definable languages.