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The perceptron strikes back

Author: Richard Beigel; Nick Reingold; Daniel Spielman
Publisher: New Haven, Conn. : Yale University, Dept. of Computer Science, [1990]
Series: Yale University.; Department of Computer Science.; Technical report
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Abstract: "We show that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, every language recognized by a depth-d AC⁰ circuit is decidable by a probabilistic perceptron of size 2[superscript O(log 5d n)] and order  Read more...
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Document Type: Book
All Authors / Contributors: Richard Beigel; Nick Reingold; Daniel Spielman
OCLC Number: 25999718
Notes: "September 11, 1990."
Description: 7 leaves ; 28 cm.
Series Title: Yale University.; Department of Computer Science.; Technical report
Responsibility: Richard Beigel, Nick Reingold, Daniel Spielman.

Abstract:

Abstract: "We show that circuits composed of a symmetric gate at the root with AND-OR subcircuits of constant depth can be simulated by probabilistic depth-2 circuits with essentially the same symmetric gate at the root and AND gates of small fanin at the bottom. In particular, every language recognized by a depth-d AC⁰ circuit is decidable by a probabilistic perceptron of size 2[superscript O(log 5d n)] and order O(log[superscript 5d] n) that uses O(log³n) probabilistic bits. As a corollary, we present a new proof that depth-d AND-OR circuits computing the parity of n binary inputs require size 2[superscript n omega](1/d)]."

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