Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T13:50:29.731Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.