The #CSP Dichotomy is Decidable

Dyer, Martin; Richerby, David

doi:10.4230/LIPIcs.STACS.2011.261

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The #CSP Dichotomy is Decidable

Authors Martin Dyer, David Richerby

Part of: Volume: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
Publication Date: 2011-03-11

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DOI: 10.4230/LIPIcs.STACS.2011.261
URN: urn:nbn:de:0030-drops-30161

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Keywords

constraint satisfaction problem
counting problems
complexity dichotomy
decidability

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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.

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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

Author Details

Martin Dyer

David Richerby

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