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

Bernd Borchert; Dietrich Kuske; Frank Stephan

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 33, Issue: 3, page 259-269
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Borchert, Bernd, Kuske, Dietrich, and Stephan, Frank. "On Existentially First-Order Definable Languages and Their Relation to NP." RAIRO - Theoretical Informatics and Applications 33.3 (2010): 259-269. <http://eudml.org/doc/222021>.

@article{Borchert2010,
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. },
author = {Borchert, Bernd, Kuske, Dietrich, Stephan, Frank},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Leaf languages; NP; first-order definable languages.; polynomial-time hierarchy; first-order logic; existential definability; regular language; automata},
language = {eng},
month = {3},
number = {3},
pages = {259-269},
publisher = {EDP Sciences},
title = {On Existentially First-Order Definable Languages and Their Relation to NP},
url = {http://eudml.org/doc/222021},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Borchert, Bernd
AU - Kuske, Dietrich
AU - Stephan, Frank
TI - On Existentially First-Order Definable Languages and Their Relation to NP
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 3
SP - 259
EP - 269
AB - 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.
LA - eng
KW - Leaf languages; NP; first-order definable languages.; polynomial-time hierarchy; first-order logic; existential definability; regular language; automata
UR - http://eudml.org/doc/222021
ER -

References

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  7. 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.  
  8. R. McNaughton and S. Papert, Counter-Free Automata, MIT Press, Cambridge, MA (1971).  
  9. J.-E. Pin and P. Weil, Polynomial closure and unambiguous product. Theory Comput. Systems30 (1997) 383-422.  Zbl0872.68119
  10. H. Straubing, Finite Automata, Formal Logic, and Circuit Complexity, Birkhäuser, Boston (1994).  
  11. W. Thomas, Classifying regular events in symbolic logic. J. Comput. System Sci.25 (1982) 360-376.  Zbl0503.68055
  12. S. Toda, PP is as hard as the Polynomial-Time Hierarchy. SIAM J. Comput.20 (1991) 865-877.  Zbl0733.68034

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