Testing to see if a Boolean circuit computes the identically zero function is a fundamental problem in computational complexity. Known as the SAT (for satisfiability) problem, it is the first ...

Arithmetic circuit complexity investigates the computational resources required to evaluate polynomial functions via networks of arithmetic operations. At its core, this field seeks to classify ...

We study depth three arithmetic circuits with bounded top fanin. We give the first deterministic polynomial time blackbox identity test for depth three circuits with bounded top fanin over the field ...

We prove that if A is an algebra over a field with at least k elements, and A satisfies xk = 0, then An, the ring of n-by-n matrices over A, satisfies xq = 0, where q = kn2 + 1. Theorem 1.3 ...

Finding out the exact computational complexity of Polynomial Identity Testing is one of the most important unsolved problems in this subject area. Prof. Saxena took a step forward in solving this ...

It is shown that if α denotes an n × n antisymmetric matrix of operators α pq ,p,q = 1, 2, …, n, which satisfy the commutation relations characteristic of the Lie algebra of SO(n), then α satisfies an ...

Abstract: We give a deterministic polynomial time algorithm for polynomial identity testing in the following two cases: 1. Non commutative arithmetic formulas: the algorithm gets as an input an ...

Abstract: In this paper we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that ...

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We introduce a new and natural algebraic proof system, whose complexity measure is essentially the algebraic circuit size of Nullstellensatz certificates. This enables us to exhibit close connections ...

Using an elementary approach involving the Euler Beta function and the binomial theorem, we derive two polynomial identities; one of which is a generalization of a known polynomial identity. Two ...