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

Abstract

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].