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Paper:

TR16-171 | 3rd November 2016 23:07

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

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TR16-171
Authors: Daniel Minahan, Ilya Volkovich
Publication: 4th November 2016 03:29
Downloads: 703
Keywords: 


Abstract:

In this paper we study the identity testing problem of \emph{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 $\set{+,\times}$ 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 \cite{ShpilkaVolkovich15a}.



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