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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-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.

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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References

Beigel, R. and Gill, J., Counting classes: Thresholds, parity, mods, and fewness. Theoret. Comput. Sci. 103 (1992) 3-23. CrossRef
Borchert, B., On the acceptance power of regular languages. Theoret. Comput. Sci. 148 (1995) 207-225. CrossRef
Bovet, D.P., Crescenzi, P. and Silvestri, R., A uniform approach to define complexity classes. Theoret. Comput. Sci. 104 (1992) 263-283. CrossRef
Burtschick, H.-J. and Vollmer, H., Lindström Quantifiers and Leaf Language Definability. Internat. J. Found. Comput. Sci. 9 (1998) 277-294. CrossRef
Cai, J.-Y., Gundermann, T., Hartmanis, J., Hemachandra, L.A., Sewelson, V., Wagner, K. and Wechsung, G., The Boolean Hierarchy I: Structural properties. SIAM J. Comput. 17 (1988) 1232-1252. CrossRef
Chang, R., Kadin, J. and Rohatgi, P., On unique satisfiability and the threshold behaviour of randomized reductions. J. Comput. System Sci. 50 (1995) 359-373. CrossRef
U. Hertrampf, C. Lautemann, T. Schwentick, H. Vollmer and K. Wagner, On the power of polynomial-time bit-computations, In: Proc. 8th Structure in Complexity Theory Conference, IEEE Computer Society Press (1993) 200-207.
R. McNaughton and S. Papert, Counter-Free Automata, MIT Press, Cambridge, MA (1971).
Pin, J.-E. and Weil, P., Polynomial closure and unambiguous product. Theory Comput. Systems 30 (1997) 383-422. CrossRef
H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhäuser, Boston (1994).
Thomas, W., Classifying regular events in symbolic logic. J. Comput. System Sci. 25 (1982) 360-376. CrossRef
PP, S. Toda is as hard as the Polynomial-Time Hierarchy. SIAM J. Comput. 20 (1991) 865-877.