Approximate counting by hashing in bounded arithmetic
Emil Jeřábek
Source: J. Symbolic Logic Volume 74, Issue 3 (2009), 829-860.
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.
Primary Subjects: 03F30
Keywords: Bounded arithmetic; approximate counting; universal hashing
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1245158087
Digital Object Identifier: doi:10.2178/jsl/1245158087
