The \#CSP Dichotomy is Decidable

Martin Dyer (1) , David Richerby (1)

1 School of Computing [Leeds]

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 \numpc{}, 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{}.

Mots clés: Constraint satisfaction problem; counting problems; complexity dichotomy; decidability.; decidability

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Martin Dyer, David Richerby. The \#CSP Dichotomy is Decidable. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.261-272. ⟨hal-00573600⟩