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September 2009 Approximate counting by hashing in bounded arithmetic
Emil Jeřábek
J. Symbolic Logic 74(3): 829-860 (September 2009). DOI: 10.2178/jsl/1245158087

Abstract

We show how to formalize approximate counting via hash functions insubsystems of bounded arithmetic, using variants of the weakpigeonhole principle. We discuss several applications, including aproof of the tournament principle, and an improvement on the knownrelationship of the collapse of the bounded arithmetic hierarchy tothe collapse of the polynomial-time hierarchy.

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Emil Jeřábek. "Approximate counting by hashing in bounded arithmetic." J. Symbolic Logic 74 (3) 829 - 860, September 2009. https://doi.org/10.2178/jsl/1245158087

Information

Published: September 2009
First available in Project Euclid: 16 June 2009

zbMATH: 1180.03055
MathSciNet: MR2548464
Digital Object Identifier: 10.2178/jsl/1245158087

Subjects:
Primary: 03F30

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 3 • September 2009
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