2012 IEEE 27th Conference on Computational Complexity (2011)

San Jose, California USA

June 8, 2011 to June 11, 2011

ISSN: 1093-0159

ISBN: 978-0-7695-4411-3

pp: 115-125

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2011.36

ABSTRACT

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

CITATION

Ryan Williams,
"Non-uniform ACC Circuit Lower Bounds",

*2012 IEEE 27th Conference on Computational Complexity*, vol. 00, no. , pp. 115-125, 2011, doi:10.1109/CCC.2011.36