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Approximate counting in bounded arithmetic

Published online by Cambridge University Press:  12 March 2014

Emil Jeřábek
Emil Jeřábek*
Affiliation:
Institute of Mathematics, AS CR, Žitná 25, 115 67 Praha 1, Czech Republic. E-mail: [email protected], URL: http://math.cas.cz/~jerabek/index.html
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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).

Keywords

Bounded arithmeticpigeonhole principlecountingrandomized algorithms
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 3 , September 2007 , pp. 959 - 993
Copyright
Copyright © Association for Symbolic Logic 2007

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