The Complexity of Weighted Boolean #CSP Modulo $k$

Heng Guo (1) , Sangxia Huang (2) , Pinyan Lu (3) , Mingji Xia (4)

1 CS - Department of Computer Sciences [Madison]
2 KTH - KTH Royal Institute of Technology [Stockholm]
3 Microsoft Research Asia
4 Institute of Software

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 $k$.

Mots clés: #CSP; dichotomy theorem; counting problems; computational complexity

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Heng Guo, Sangxia Huang, Pinyan Lu, Mingji Xia. The Complexity of Weighted Boolean #CSP Modulo $k$. Symposium on Theoretical Aspects of Computer Science (STACS2011), Mar 2011, Dortmund, Germany. pp.249-260. ⟨hal-00573644⟩