Journal of Symbolic Logic

Approximate counting in bounded arithmetic

Emil Jeřábek

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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).

Article information

Source
J. Symbolic Logic, Volume 72, Issue 3 (2007), 959-993.

Dates
First available in Project Euclid: 2 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1191333850

Digital Object Identifier
doi:10.2178/jsl/1191333850

Mathematical Reviews number (MathSciNet)
MR2354909

Zentralblatt MATH identifier
1123.03051

Subjects
Primary: 03F30: First-order arithmetic and fragments
Secondary: 68W20: Randomized algorithms

Keywords
Bounded arithmetic pigeonhole principle counting randomized algorithms

Citation

Jeřábek, Emil. Approximate counting in bounded arithmetic. J. Symbolic Logic 72 (2007), no. 3, 959--993. doi:10.2178/jsl/1191333850. https://projecteuclid.org/euclid.jsl/1191333850


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