TR09-073 Authors: Vikraman Arvind, Pushkar Joglekar, Srikanth Srinivasan

Publication: 6th September 2009 19:28

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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 the noncommutative settings.

2. We prove hardness-randomness tradeoffs for identity testing constant-width commutative circuits analogous to [KI03,DSY08].