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Approximate counting by hashing in bounded arithmetic

Published online by Cambridge University Press:  12 March 2014

Emil Jeřábek
Emil Jeřábek*
Affiliation:
Institute of Mathematics of the Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, E-mail: [email protected], URL: http://math.cas.cz/~jerabek
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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.

Keywords

Bounded arithmeticapproximate countinguniversal hashing03F30
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 829 - 860
Copyright
Copyright © Association for Symbolic Logic 2009

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