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Non-uniform ACC Circuit Lower Bounds

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1 Author(s)
Williams, R. ; IBM Almaden Res. Center, San Jose, CA, USA

The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MODm gates, where m >; 1 is an arbitrary constant. We prove: 1. NTIME[2n] does not have non-uniform ACC circuits of polynomial size. The size lower bound can be strengthened to quasi-polynomials and other less natural functions. 2. ENP, the class of languages recognized in 2O(n) time with an NP oracle, doesn't have non-uniform ACC circuits of 2no(1) size. The lower bound gives a size-depth tradeoff: for every d, m there is a δ >; 0 such that ENP doesn't have s depth-d ACC circuits of size 2 with MODm gates. Previously, it was not known whether EXPNP had depth-3 polynomial size circuits made out of only MOD6 gates. The high-level strategy is to design faster algorithms for the circuit satisfiability problem over ACC circuits, then prove that such algorithms can be applied to obtain the above lower bounds.

Published in:

Computational Complexity (CCC), 2011 IEEE 26th Annual Conference on

Date of Conference:

8-11 June 2011