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 very similar to the one for the complex weighted Boolean #CSP, found by [Cai, Lu and Xia, STOC 2009]. Then we further extend the result to an arbitrary integer k.
#CSP
dichotomy theorem
counting problems
computational complexity
249-260
Regular Paper
Heng
Guo
Heng Guo
Sangxia
Huang
Sangxia Huang
Pinyan
Lu
Pinyan Lu
Mingji
Xia
Mingji Xia
10.4230/LIPIcs.STACS.2011.249
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