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TR16-171 | 3rd November 2016 23:07
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#### Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas

**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}.