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Approximate counting by hashing in bounded arithmetic
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SYSNO ASEP 0326451 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Approximate counting by hashing in bounded arithmetic Title Aproximativní počítání pomocí hashování v omezené aritmetice Author(s) Jeřábek, Emil (MU-W) RID, SAI, ORCID Source Title Journal of Symbolic Logic. - : Cambridge University Press - ISSN 0022-4812
Roč. 74, č. 3 (2009), s. 829-860Number of pages 32 s. Language eng - English Country US - United States Keywords bounded arithmetic ; approximate counting ; universal hashing Subject RIV BA - General Mathematics R&D Projects IAA1019401 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000269571100006 Annotation We show how to formalize approximate counting via hash functions in subsystems of bounded arithmetic, using variants of the weak pigeonhole principle. We discuss several appications, including a proof of the tournament principle, and an improvement on the known relationship of the collapse of the bounded arithmetic hierarchy tot he collapse of the polynomial-time hierarchy. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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