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)


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).


Boolean Function Constraint Satisfaction Problem Isomorphism Type Boolean Circuit Constraint Language 
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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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