The complexity of satisfiability problems: Refining Schaefer's theorem
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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). A similar classification holds for quantified constraint satisfaction problems.
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article
article
article
Date
2009-01-01