More on Noncommutative Polynomial Identity Testing

We continue the study of noncommutative polynomial identity testing initiated by Raz and Shpilka and present efficient algorithms for the following problems in the noncommutative model: Polynomial identity testing: The algorithm gets as an input an arithmetic circuit with the promise that the polynomial it computes has small degree (for instance, a circuit of logarithmic depth or an arithmetic formula) and determines whether or not the output of the circuit is identically zero (as a formal expression). Unlike the algorithm by Raz and Shpilka, our algorithm is black-box (but randomized with one-sided error) and evaluates the circuit over the ring of matrices. In addition, we present query complexity lower bounds for identity testing and explore the possibility of derandomizing our algorithm. The analysis of our algorithm uses a noncommutative variant of the Schwartz-Zippel test. Minimizing algebraic branching programs: The algorithm gets as an input an algebraic branching program (ABP...

• Type: Conference
• Year: 2005
• Where: COCO
• Authors: Andrej Bogdanov, Hoeteck Wee
• Keywords: Algorithm, COCO 2005, Noncommutative Polynomial Identity, Polynomial Identity Testing