Approximate counting in bounded arithmetic

Emil Jeřábek

doi:10.2178/jsl/1191333850

Abstract

We develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV₁ + dWPHP(PV).

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Emil Jeřábek. "Approximate counting in bounded arithmetic." J. Symbolic Logic 72 (3) 959 - 993, September 2007. https://doi.org/10.2178/jsl/1191333850

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Published: September 2007

First available in Project Euclid: 2 October 2007

zbMATH: 1123.03051

MathSciNet: MR2354909

Digital Object Identifier: 10.2178/jsl/1191333850

Subjects:

Primary: 03F30

Secondary: 68W20

Keywords: bounded arithmetic , counting , pigeonhole principle , randomized algorithms

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