On Lower Bounds for Constant Width Arithmetic Circuits
V. Arvind, Pushkar S. Joglekar, Srikanth Srinivasan · arXiv (Cornell University) · 2009
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 constantdepth hierarchies of monotone arithmetic circuits are infinite, both in the commutative and the noncommutative settings. 2. We prove hardness-randomness tradeoffs for identity testing constant-width commutative circuits analogous to [KI03,DSY08].