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The Complexity of Weighted Boolean #CSP Modulo k

Authors Heng Guo, Sangxia Huang, Pinyan Lu, Mingji Xia



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LIPIcs.STACS.2011.249.pdf
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Heng Guo
Sangxia Huang
Pinyan Lu
Mingji Xia

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Heng Guo, Sangxia Huang, Pinyan Lu, and Mingji Xia. The Complexity of Weighted Boolean #CSP Modulo k. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 249-260, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)
https://doi.org/10.4230/LIPIcs.STACS.2011.249

Abstract

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.
Keywords
  • #CSP
  • dichotomy theorem
  • counting problems
  • computational complexity

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