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The Complexity of Planar Boolean #CSP with Complex Weights
[chapter]
2013
Lecture Notes in Computer Science
We prove a complexity dichotomy theorem for symmetric complex-weighted Boolean #CSP when the constraint graph of the input must be planar. The problems that are #P-hard over general graphs but tractable over planar graphs are precisely those with a holographic reduction to matchgates. This generalizes a theorem of Cai, Lu, and Xia for the case of real weights. We also obtain a dichotomy theorem for a symmetric arity 4 signature with complex weights in the planar Holant framework, which we use
doi:10.1007/978-3-642-39206-1_44
fatcat:ormuxbgvfjbr5kuve4ybzzgjmi