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PP is closed under intersection

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
Database:WorldCat
Summary:
Abstract: "In his seminal paper on probabilistic Turing machines, Gill [Gil77] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. In fact, PP is closed under polynomial-time multilinear reductions. In circuits, this allows us to combine several threshold gates into a single threshold gate, while increasing depth by only a constant. Consequences in
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Details

Document Type: Book
All Authors / Contributors: Richard Beigel; Nick Reingold; Daniel Spielman
OCLC Number: 25999725
Notes: "June 1990."
Description: 13 pages ; 28 cm.
Series Title: Yale University.; Department of Computer Science.; Technical report
Responsibility: Richard Beigel, Nick Reingold, Daniel Spielman.

Abstract:

Abstract: "In his seminal paper on probabilistic Turing machines, Gill [Gil77] asked whether the class PP is closed under intersection and union. We give a positive answer to this question. In fact, PP is closed under polynomial-time multilinear reductions. In circuits, this allows us to combine several threshold gates into a single threshold gate, while increasing depth by only a constant. Consequences in complexity theory include definite collapse and plausible separation of certain query hierarchies over PP.

Consequences in the study of circuits include the simulation of circuits with a small number of threshold gates by circuits having only a single threshold gate at the root (perceptrons), and a lower bound on the number of threshold gates needed in order to compute the parity function."

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