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In this article, we study the identity testing problem of arithmetic read-once formulas (ROFs) and some related models. An ROF is a formula (a circuit whose underlying graph is a tree) in which the operations are +, 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 ROFs, 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 and Yolkovich [51].
ACM Transactions on Computation Theory (TOCT) – Association for Computing Machinery
Published: May 23, 2018
Keywords: Arithmetic circuit
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