Deterministic Identity Testing of Read-Once Algebraic Branching Programs

In this paper we study polynomial identity testing of sums of k read-once algebraic branching programs (Σk-RO-ABPs), generalizing the work of Shpilka and Volkovich [1, 2], who considered sums of k read-once formulas (Σk-RO-formulas). We show that Σk-RO-ABPs are strictly more powerful than Σk-RO-formulas, for any k ≤ ⌊n/2⌋, where n is the number of variables. Nevertheless, as a starting observation, we show that the generator given in [2] for testing a single RO-formula also works against a single RO-ABP. For the main technical part of this paper, we develop a property of polynomials called alignment. Using this property in conjunction with the hardness of representation approach of [1, 2], we obtain the following results for identity testing Σk-RO-ABPs, provided the underlying field has enough elements (more than kn4 suffices):

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Maurice Jansen, Youming Qiao, Jayalal M. N. Sarma
• Keywords: ECCC 2010, Polynomial Identity Testing, Read-once Algebraic Branching, Sums