Journal of Symbolic Logic 72 (3):959 - 993 (2007)

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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)
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DOI 10.2178/jsl/1191333850
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References found in this work BETA

Bounded Arithmetic and the Polynomial Hierarchy.Jan Krajíček, Pavel Pudlák & Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52 (1-2):143-153.
The Strength of Sharply Bounded Induction.Emil Jeřábek - 2006 - Mathematical Logic Quarterly 52 (6):613-624.
Dual Weak Pigeonhole Principle, Boolean Complexity, and Derandomization.Emil Jeřábek - 2004 - Annals of Pure and Applied Logic 129 (1-3):1-37.
Relating the Bounded Arithmetic and Polynomial Time Hierarchies.Samuel R. Buss - 1995 - Annals of Pure and Applied Logic 75 (1-2):67-77.
Structures Interpretable in Models of Bounded Arithmetic.Neil Thapen - 2005 - Annals of Pure and Applied Logic 136 (3):247-266.

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Citations of this work BETA

Uniform Proofs of ACC Representations.Sam Buss - 2017 - Archive for Mathematical Logic 56 (5-6):639-669.
Circuit Lower Bounds in Bounded Arithmetics.Ján Pich - 2015 - Annals of Pure and Applied Logic 166 (1):29-45.

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