The #CSP Dichotomy is Decidable

نویسندگان

  • Martin E. Dyer
  • David Richerby
چکیده

Bulatov (2008) and Dyer and Richerby (2010) have established the following dichotomy for the counting constraint satisfaction problem (#CSP): for any constraint language Γ, the problem of computing the number of satisfying assignments to constraints drawn from Γ is either in FP or is #P-complete, depending on the structure of Γ. 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. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Effective Dichotomy for the Counting Constraint Satisfaction Problem

Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language Γ, a fixed, finite set of relations over a finite domain D. An instance of the problem uses these relations to constrain an arbitrarily large finite set of variables. Bulatov showed that the problem of counting the satisfying assignments of instanc...

متن کامل

Non-negative Weighted #CSPs: An Effective Complexity Dichotomy

We prove a complexity dichotomy theorem for all non-negative weighted counting Constraint Satisfaction Problems (CSP). This caps a long series of important results on counting problems including unweighted and weighted graph homomorphisms [19, 8, 18, 12] and the celebrated dichotomy theorem for unweighted #CSP [6, 4, 21, 22]. Our dichotomy theorem gives a succinct criterion for tractability. If...

متن کامل

The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable

Given a fixed constraint language Γ , the conservative CSP over Γ (denoted by c-CSP(Γ )) is a variant of CSP(Γ ) where the domain of each variable can be restricted arbitrarily. In [5] a dichotomy has been proven for conservative CSP: for every fixed language Γ , c-CSP(Γ ) is either in P or NP-complete. However, the characterization of conservatively tractable languages is of algebraic nature a...

متن کامل

A combinatorial constraint satisfaction problem dichotomy classification conjecture

We further generalise a construction – the fibre construction – that was developed in an earlier paper of the first two authors. The extension in this paper gives a polynomial-time reduction of CSP(H) for any relational system H to CSP(P ) for any relational system P that meets a certain technical partition condition, that of being K3-partitionable. Moreover, we define an equivalent condition o...

متن کامل

The Complexity of Weighted Boolean #CSP Modulo k

We prove a complexity dichotomy theorem for counting weighted Boolean CSP modulo k for any positive integer k > 1. This generalizes a theorem by Faben for the unweighted setting. In the weighted setting, there are new interesting tractable problems. We first prove a dichotomy theorem for the finite field case where k is a prime. It turns out that the dichotomy theorem for the finite field is ve...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011