Deterministic polynomial identity tests for multilinear bounded-read formulae

We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Our algorithm runs in time sO(1) ·nkO(k) , where s denotes the size of the formula, n denotes the number of variables, and k bounds the number of occurrences of each variable. Before our work no subexponential-time deterministic algorithm was known for this class of formulae. We also present a deterministic algorithm that works in a blackbox fashion and runs in time nkO(k)+O(k log n) in general, and time nkO(k2)+O(kD) for depth D. Finally, we extend our results and allow the inputs to be replaced with sparse polynomials. Our results encompass recent deterministic identity tests for sums of a constant number of read-once formulae, and for multilinear depth-four formulae. Keywords. Derandomization, Identity Testing, Arithmet...

• Type: Journal
• Year: 2015
• Where: CC
• Authors: Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich
• Keywords: CC 2015, System Software