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.CCC.2017.32
URN: urn:nbn:de:0030-drops-75128
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7512/
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Minahan, Daniel ; Volkovich, Ilya

Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas

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LIPIcs-CCC-2017-32.pdf (0.5 MB)

Abstract

In this paper we study the identity testing problem of arithmetic read-once formulas (ROF) and some related models. A read-once formula is formula (a circuit whose underlying graph is a tree) in which the operations are {+,x} and such that every input variable labels at most one leaf. We obtain the first polynomial-time deterministic identity testing algorithm that operates in the black-box setting for read-once formulas, as well as some other related models. As an application, we obtain the first polynomial-time deterministic reconstruction algorithm for such formulas. Our results are obtained by improving and extending the analysis of the algorithm of [Shpilka-Volkovich, 2015]

BibTeX - Entry

@InProceedings{minahan_et_al:LIPIcs:2017:7512,
  author =	{Daniel Minahan and Ilya Volkovich},
  title =	{{Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{Ryan O'Donnell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7512},
  URN =		{urn:nbn:de:0030-drops-75128},
  doi =		{10.4230/LIPIcs.CCC.2017.32},
  annote =	{Keywords: Derandomization, Read-Once Formulas, Identity Testing, Arithmetic Circuits, Reconstruction}
}

Keywords: Derandomization, Read-Once Formulas, Identity Testing, Arithmetic Circuits, Reconstruction
Collection: 32nd Computational Complexity Conference (CCC 2017)
Issue Date: 2017
Date of publication: 01.08.2017

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