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The #CSP Dichotomy is Decidable

Authors Martin Dyer, David Richerby



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LIPIcs.STACS.2011.261.pdf
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Martin Dyer
David Richerby

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Martin Dyer and David Richerby. The #CSP Dichotomy is Decidable. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 261-272, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.STACS.2011.261

Abstract

Bulatov (2008) and Dyer and Richerby (2010) have established the following dichotomy for the counting constraint satisfaction problem (#CSP): for any constraint language Gamma, the problem of computing the number of satisfying assignments to constraints drawn from Gamma is either in FP or is #P-complete, depending on the structure of Gamma. The principal question left open by this research was whether the criterion of the dichotomy is decidable. We show that it is; in fact, it is in NP.
Keywords
  • constraint satisfaction problem
  • counting problems
  • complexity dichotomy
  • decidability

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