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- W2147645008 abstract "The author proves in this paper that it is much harder to evaluate depth-2, size-N circuits with MOD m gates than with MOD p gates by k-party communication protocols: he shows a k-party protocol which communicates O(1) bits to evaluate circuits with MOD p gates, while evaluating circuits with MOD m gates needs Omega (N) bits, where p denotes a prime, and m a composite, non-prime power number. As a corollary, for all m, he shows a function, computable with a depth-2 circuit with MOD m gates, but not with any depth-2 circuit with MOD p gates. He proves in the second part that the GIP function by L. Babai et al. (1989) needs exponential size in n when it is computed by some depth-3 circuits, with threshold, symmetric, and MOD m gates.< <ETX xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>></ETX>" @default.
- W2147645008 created "2016-06-24" @default.
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- W2147645008 date "1992-01-01" @default.
- W2147645008 modified "2023-09-23" @default.
- W2147645008 title "Separating the communication complexities of MOD m and MOD p circuits" @default.
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- W2147645008 doi "https://doi.org/10.1109/sfcs.1992.267764" @default.
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