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

Authors Daniel Minahan, Ilya Volkovich

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Daniel Minahan
Ilya Volkovich

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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) https://doi.org/10.4230/LIPIcs.CCC.2017.32

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]

Subject Classification

Keywords
  • Derandomization
  • Read-Once Formulas
  • Identity Testing
  • Arithmetic Circuits
  • Reconstruction

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