eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2011-03-11
249
260
10.4230/LIPIcs.STACS.2011.249
article
The Complexity of Weighted Boolean #CSP Modulo k
Guo, Heng
Huang, Sangxia
Lu, Pinyan
Xia, Mingji
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol009-stacs2011/LIPIcs.STACS.2011.249/LIPIcs.STACS.2011.249.pdf
#CSP
dichotomy theorem
counting problems
computational complexity