License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2014.493
URN: urn:nbn:de:0030-drops-48665
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4866/
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Durand, Arnaud ; Mahajan, Meena ; Malod, Guillaume ; de Rugy-Altherre, Nicolas ; Saurabh, Nitin

Homomorphism Polynomials Complete for VP

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Abstract

The VP versus VNP question, introduced by Valiant, is probably the most important open question in algebraic complexity theory. Thanks to completeness results, a variant of this question, VBP versus VNP, can be succinctly restated as asking whether the permanent of a generic matrix can be written as a determinant of a matrix of polynomially bounded size. Strikingly, this restatement does not mention any notion of computational model. To get a similar restatement for the original and more fundamental question, and also to better understand the class itself, we need a complete polynomial for VP. Ad hoc constructions yielding complete polynomials were known, but not natural examples in the vein of the determinant. We give here several variants of natural complete polynomials for VP, based on the notion of graph homomorphism polynomials.

BibTeX - Entry

@InProceedings{durand_et_al:LIPIcs:2014:4866,
  author =	{Arnaud Durand and Meena Mahajan and Guillaume Malod and Nicolas de Rugy-Altherre and Nitin Saurabh},
  title =	{{Homomorphism Polynomials Complete for VP}},
  booktitle =	{34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)},
  pages =	{493--504},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-77-4},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{29},
  editor =	{Venkatesh Raman and S. P. Suresh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4866},
  URN =		{urn:nbn:de:0030-drops-48665},
  doi =		{10.4230/LIPIcs.FSTTCS.2014.493},
  annote =	{Keywords: algebraic complexity, graph homomorphism, polynomials, VP,   VNP, completeness}
}

Keywords: algebraic complexity, graph homomorphism, polynomials, VP, VNP, completeness
Collection: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)
Issue Date: 2014
Date of publication: 12.12.2014

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