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DOI: 10.4230/LIPIcs.CCC.2017.32
Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas

Authors: Daniel Minahan and Ilya Volkovich

Published in: LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017)

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]
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Daniel Minahan and Ilya Volkovich. Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{minahan_et_al:LIPIcs.CCC.2017.32,
  author =	{Minahan, Daniel and Volkovich, Ilya},
  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 =	{O'Donnell, Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.32},
  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}
}
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