A Lower Bound for Noncommutative Monotone Arithmetic Circuits

The Complexity of Two Register and Skew Arithmetic Computation

We study two register arithmetic computation and skew arithmetic circuits. Our main results are the following: • For commutative computations, we show that an exponential circuit size lower bound for a model of 2-register straight-line programs (SLPs) which is a universal model of computation (unlike width-2 algebraic branching programs that are not universal [AW11]). • For noncommutative compu...

On Lower Bounds for Constant Width Arithmetic Circuits

The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone circuit of width 2k but has no subexponential-sized monotone circuit of width k. It follows, from the definition of the polynomial, that the constant-width and the...

Lower Bounds for Resolution and Cutting Plane Proofs and Monotone Computations

We prove an exponential lower bound on the length of cutting plane proofs. The proof uses an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates. The latter result is of independent interest, since, in particular, it implies an exponential lower bound for some arithmetic circuits.

A lower bound for monotone arithmetic circuits computing O-l permanent

Arithmetic Circuit Size, Identity Testing, and Finite Automata

Let F〈x1, x2, · · · , xn〉 be the noncommutative polynomial ring over a field F, where the xi’s are free noncommuting formal variables. Given a finite automaton A with the xi’s as alphabet, we can define polynomials f(mod A) and f(div A) obtained by natural operations that we call intersecting and quotienting the polynomial f by A. Related to intersection, we also define the Hadamard product f ◦...