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DOI: 10.4230/LIPIcs.STACS.2011.249
URN: urn:nbn:de:0030-drops-30158
URL: http://drops.dagstuhl.de/opus/volltexte/2011/3015/

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

The Complexity of Weighted Boolean #CSP Modulo k

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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.

BibTeX - Entry

@InProceedings{guo_et_al:LIPIcs:2011:3015,
  author =	{Heng Guo and Sangxia Huang and Pinyan Lu and Mingji Xia},
  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 =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3015},
  URN =		{urn:nbn:de:0030-drops-30158},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2011.249},
  annote =	{Keywords: #CSP, dichotomy theorem, counting problems, computational complexity}
}

Keywords: #CSP, dichotomy theorem, counting problems, computational complexity
Seminar: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue date: 2011
Date of publication: 11.03.2011


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