Complexity of generalized satisfiability counting problems
Information and Computation
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Holographic algorithms: from art to science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The Complexity of Weighted Boolean CSP
SIAM Journal on Computing
An approximation trichotomy for Boolean #CSP
Journal of Computer and System Sciences
Approximate counting for complex-weighted Boolean constraint satisfaction problems
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
A trichotomy theorem for the approximate counting of complex-weighted bounded-degree boolean CSPs
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Approximate counting for complex-weighted Boolean constraint satisfaction problems
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Optimization, randomized approximability, and boolean constraint satisfaction problems
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
A dichotomy theorem for the approximate counting of complex-weighted bounded-degree Boolean CSPs
Theoretical Computer Science
Approximate counting for complex-weighted Boolean constraint satisfaction problems
Information and Computation
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
Theoretical Computer Science
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
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Constraint satisfaction problems (or CSPs) have been extensively studied in, e.g., artificial intelligence, database theory, graph theory, and statistical physics. A practical application often requires only an approximate value of the total number of assignments that satisfy all given Boolean constraints. There is a known trichotomy theorem for such approximate counting for (non-weighted) Boolean CSPs; namely, all such counting problems are neatly classified into three categories under polynomial-time approximation-preserving reductions. We extend this result to approximate counting for complex-weighted Boolean CSPs, provided that all unary constraints are freely available to use. This marks a significant progress in the quest for the approximation classification of all counting Boolean CSPs. To deal with complex weights, we employ proof techniques along the line of solving Holant problems. Our result also gives an approximation version of the known dichotomy theorem of the complexity of exact counting for such complex-weighted Boolean CSPs.