Hard enumeration problems in geometry and combinatorics
SIAM Journal on Algebraic and Discrete Methods
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
The effect of two cycles on the complexity of colouring by directed graphs
Discrete Applied Mathematics
Dempster's rule of combination is #P-complete (research note)
Artificial Intelligence
Hereditarily hard H-colouring problems
Selected papers of the 14th British conference on Combinatorial conference
A polynomial algorithm for homomorphisms to oriented cycles
Journal of Algorithms
Complexity of generalized satisfiability counting problems
Information and Computation
On the hardness of approximate reasoning
Artificial Intelligence
Closure properties of constraints
Journal of the ACM (JACM)
Theories of computability
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraints, consistency and closure
Artificial Intelligence
The Complexity of Planar Counting Problems
SIAM Journal on Computing
On Approximately Counting Colorings of Small Degree Graphs
SIAM Journal on Computing
Graph homomorphisms and phase transitions
Journal of Combinatorial Theory Series B
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
The complexity of counting colourings and independent sets in sparse graphs and hypergraphs
Computational Complexity
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Counting H-colorings of partial k-trees
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Towards a Dichotomy Theorem for the Counting Constraint Satisfaction Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The restrictive H-coloring problem
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
The complexity of counting homomorphisms seen from the other side
Theoretical Computer Science
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Systems of equations over finite semigroups and the #CSP dichotomy conjecture
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
A new line of attack on the dichotomy conjecture
Proceedings of the forty-first annual ACM symposium on Theory of computing
A Computational Proof of Complexity of Some Restricted Counting Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Classification of a Class of Counting Problems Using Holographic Reductions
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Proceedings of the forty-second ACM symposium on Theory of computing
A computational proof of complexity of some restricted counting problems
Theoretical Computer Science
Spin systems on graphs with complex edge functions and specified degree regularities
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Guest column: complexity dichotomies of counting problems
ACM SIGACT News
Gadgets and anti-gadgets leading to a complexity dichotomy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Journal of Computer and System Sciences
The complexity of weighted and unweighted #CSP
Journal of Computer and System Sciences
Spin systems on k-regular graphs with complex edge functions
Theoretical Computer Science
A complete dichotomy rises from the capture of vanishing signatures: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of planar boolean #CSP with complex weights
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
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The Counting Constraint Satisfaction Problem (#CSP) can be expressed as follows: given a set of variables, a set of values that can be taken by the variables, and a set of constraints specifying some restrictions on the values that can be taken simultaneously by some variables, determine the number of assignments of values to variables that satisfy all the constraints. The #CSP provides a general framework for numerous counting combinatorial problems including counting satisfying assignments to a propositional formula, counting graph homomorphisms, graph reliability and many others. This problem can be parametrized by the set of relations that may appear in a constraint. In this paper we start a systematic study of subclasses of the #CSP restricted in this way. The ultimate goal of this investigation is to distinguish those restricted subclasses of the #CSP which are solvable in polynomial time from those which are not. We show that the complexity of any restricted #CSP class on a finite domain can be deduced from the properties of polymorphisms of the allowed constraints, similar to that for the decision constraint satisfaction problem. Then we prove that if a subclass of the #CSP is solvable in polynomial time, then constraints allowed by the class satisfy some very restrictive condition: they need to have a Mal'tsev polymorphism, that is a ternary operation m(x,y,z) such that m(x,y,y)=m(y,y,x)=x. This condition uniformly explains many existing complexity results for particular cases of the #CSP, including the dichotomy results for the problem of counting graph homomorphisms, and it allows us to obtain new results.