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The Complexity of Satisfiability Problems: Refining Schaefer’s Theorem

  • Eric Allender
  • Michael Bauland
  • Neil Immerman
  • Henning Schnoor
  • Heribert Vollmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

Schaefer proved in 1978 that the Boolean constraint satisfaction problem for a given constraint language is either in P or is NP-complete, and identified all tractable cases. Schaefer’s dichotomy theorem actually shows that there are at most two constraint satisfaction problems, up to polynomial-time isomorphism (and these isomorphism types are distinct if and only if P ≠ NP). We show that if one considers AC0 isomorphisms, then there are exactly six isomorphism types (assuming that the complexity classes NP, P, ⊕L, NL, and L are all distinct).

Keywords

Boolean Function Constraint Satisfaction Problem Isomorphism Type Boolean Circuit Constraint Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Eric Allender
    • 1
  • Michael Bauland
    • 2
  • Neil Immerman
    • 3
  • Henning Schnoor
    • 2
  • Heribert Vollmer
    • 2
  1. 1.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.Theoretische InformatikUniversität HannoverHannoverGermany
  3. 3.Department of Computer and Information ScienceUniversity of MassachusettsAmherstUSA

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