Improved Polynomial Identity Testing for Read-Once Formulas

An arithmetic read-once formula (ROF for short) 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. A preprocessed ROF (PROF for short) is a ROF in which we are allowed to replace each variable xi with a univariate polynomial Ti(xi). In this paper we study the problems of giving deterministic identity testing and reconstruction algorithms for preprocessed ROFs. In particular we obtain the following results.

• Type: Conference
• Year: 2009
• Where: APPROX
• Authors: Amir Shpilka, Ilya Volkovich
• Keywords: Algorithms, APPROX 2009, Arithmetic Read-once Formula, Input Variable Labels, Preprocessed Rofs