Journal of Symbolic Logic

Approximate counting in bounded arithmetic

Emil Jeřábek

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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

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

First available in Project Euclid: 2 October 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Bounded arithmetic pigeonhole principle counting randomized algorithms


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

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