The complexity of satisfiability problems: Refining Schaefer's theorem
Publication Date
2009
Journal or Book Title
JOURNAL OF COMPUTER AND SYSTEM SCIENCES
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.
DOI
https://doi.org/10.1016/j.jcss.2008.11.001
Pages
245-254
Volume
75
Issue
4
Recommended Citation
Allender, E; Bauland, M; Immerman, N; Schnoor, H; and Vollmer, H, "The complexity of satisfiability problems: Refining Schaefer's theorem" (2009). JOURNAL OF COMPUTER AND SYSTEM SCIENCES. 558.
https://doi.org/10.1016/j.jcss.2008.11.001