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• W2106793914 abstract "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[2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sup> ] 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. E <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>NP</sup> , the class of languages recognized in 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>O(n)</sup> time with an NP oracle, doesn't have non-uniform ACC circuits of 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>no(1)</sup> size. The lower bound gives a size-depth tradeoff: for every d, m there is a δ >; 0 such that E <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>NP</sup> doesn't have s depth-d ACC circuits of size 2 <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>nδ</sup> with MOD <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>m</sub> gates. Previously, it was not known whether EXP <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>NP</sup> had depth-3 polynomial size circuits made out of only MOD <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>6</sub> 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." @default.
• W2106793914 created "2016-06-24" @default.
• W2106793914 creator A5063871533 @default.
• W2106793914 date "2011-06-01" @default.
• W2106793914 modified "2023-09-27" @default.
• W2106793914 title "Non-uniform ACC Circuit Lower Bounds" @default.
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• W2106793914 doi "https://doi.org/10.1109/ccc.2011.36" @default.
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