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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 in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several applications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy to the 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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