On Lower Bounds for Constant Width Arithmetic Circuits [article]

V. Arvind, Pushkar S. Joglekar, Srikanth Srinivasan
2009 arXiv   pre-print
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 constant-depth hierarchies of monotone arithmetic circuits are infinite, both in the commutative and
more » ... he noncommutative settings. 2. We prove hardness-randomness tradeoffs for identity testing constant-width commutative circuits analogous to [KI03,DSY08].
arXiv:0907.3780v2 fatcat:s54xuq2nwba45pjcnw23bkflhi