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2011 26th Annual IEEE Conference on Computational Complexity
Non-uniform ACC Circuit Lower Bounds
San Jose, California USA
June 08-June 11
ISBN: 978-0-7695-4411-3
The class ACC consists of circuit families with constant depth over unbounded fan-in AND, OR, NOT, and MOD$m$ gates, where $m > 1$ is an arbitrary constant. We prove:- $NTIME[2^n]$ 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.- $E^{NP}$, the class of languages recognized in $2^{O(n)}$ time with an $NP$ oracle, doesn't have non-uniform ACC circuits of $2^{n^{o(1)}}$ size. The lower bound gives a size-depth tradeoff: for every $d$, $m$ there is a $\delta > 0$ such that $E^{NP}$ doesn't have depth-$d$ ACC circuits of size $2^{n^{\delta}}$ with MOD$m$ gates.Previously, it was not known whether $EXP^{NP}$ 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.
Index Terms:
circuit complexity, NEXP, ACC, non-uniform computation
Ryan Williams, "Non-uniform ACC Circuit Lower Bounds," ccc, pp.115-125, 2011 26th Annual IEEE Conference on Computational Complexity, 2011
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