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DOI: 10.4230/LIPIcs.STACS.2012.362
URN: urn:nbn:de:0030-drops-34240
URL: http://drops.dagstuhl.de/opus/volltexte/2012/3424/
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Fournier, Hervé ; Malod, Guillaume ; Mengel, Stefan

Monomials in arithmetic circuits: Complete problems in the counting hierarchy

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Abstract

We consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting hierarchy which had few or no known natural complete problems before. We also study these questions for circuits computing multilinear polynomials.

BibTeX - Entry

@InProceedings{fournier_et_al:LIPIcs:2012:3424,
  author =	{Herv{\'e} Fournier and Guillaume Malod and Stefan Mengel},
  title =	{{Monomials in arithmetic circuits: Complete problems in the counting hierarchy}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{362--373},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3424},
  URN =		{urn:nbn:de:0030-drops-34240},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2012.362},
  annote =	{Keywords: arithmetic circuits, counting problems, polynomials}
}

Keywords: arithmetic circuits, counting problems, polynomials
Seminar: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012


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