Journal of Symbolic Logic

Approximate counting by hashing in bounded arithmetic

Emil Jeřábek

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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.

Article information

J. Symbolic Logic, Volume 74, Issue 3 (2009), 829-860.

First available in Project Euclid: 16 June 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F30: First-order arithmetic and fragments

Bounded arithmetic approximate counting universal hashing


Jeřábek, Emil. Approximate counting by hashing in bounded arithmetic. J. Symbolic Logic 74 (2009), no. 3, 829--860. doi:10.2178/jsl/1245158087.

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