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.
@InProceedings{guo_et_al:LIPIcs.STACS.2011.249, author = {Guo, Heng and Huang, Sangxia and Lu, Pinyan and Xia, Mingji}, title = {{The Complexity of Weighted Boolean #CSP Modulo k}}, booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)}, pages = {249--260}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-25-5}, ISSN = {1868-8969}, year = {2011}, volume = {9}, editor = {Schwentick, Thomas and D\"{u}rr, Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.249}, URN = {urn:nbn:de:0030-drops-30158}, doi = {10.4230/LIPIcs.STACS.2011.249}, annote = {Keywords: #CSP, dichotomy theorem, counting problems, computational complexity} }
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