Journal of Symbolic Logic

Approximate counting by hashing in bounded arithmetic

Emil Jeřábek

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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.

Article information

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

Dates
First available in Project Euclid: 16 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1245158087

Digital Object Identifier
doi:10.2178/jsl/1245158087

Mathematical Reviews number (MathSciNet)
MR2548464

Zentralblatt MATH identifier
1180.03055

Subjects
Primary: 03F30: First-order arithmetic and fragments

Keywords
Bounded arithmetic approximate counting universal hashing

Citation

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


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