Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 74, Issue 3 (2009), 829-860.
Approximate counting by hashing in bounded arithmetic
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.
J. Symbolic Logic, Volume 74, Issue 3 (2009), 829-860.
First available in Project Euclid: 16 June 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03F30: First-order arithmetic and fragments
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