Complexity of generalized satisfiability counting problems
Information and Computation
Quantum Circuits That Can Be Simulated Classically in Polynomial Time
SIAM Journal on Computing
On Counting Independent Sets in Sparse Graphs
SIAM Journal on Computing
Theoretical Computer Science
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
Signature Theory in Holographic Algorithms
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Holant problems and counting CSP
Proceedings of the forty-first 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
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Approximation complexity of complex-weighted degree-two counting constraint satisfaction problems
Theoretical Computer Science
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We determine the complexity of approximate counting of the total weight of assignments for complex-weighted Boolean constraint satisfaction problems (or CSPs), particularly, when degrees of instances are bounded from above by a given constant, provided that all arity-1 (or unary) constraints are freely available. All degree-1 counting CSPs are solvable in polynomial time. When the degree is more than 2, we present a trichotomy theorem that classifies all bounded-degree counting CSPs into only three categories. This classification extends to complex-weighted problems an earlier result on the complexity of the approximate counting of bounded-degree unweighted Boolean CSPs. The framework of the proof of our trichotomy theorem is based on Cai's theory of signatures used for holographic algorithms. For the degree-2 problems, we show that they are as hard to approximate as complex Holant problems.