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### Paper:

TR01-030 | 25th April 2001 00:00

#### S_2^p \subseteq ZPP^{NP}

TR01-030
Authors: Jin-Yi Cai
Publication: 26th April 2001 14:15
Keywords:

Abstract:

We show that the class ${\rm S}_2^p$ is a subclass of
${{\rm ZPP}^{\rm NP}}$. The proof uses universal hashing, approximate counting
and witness sampling. As a consequence, a collapse first noticed by
Samik Sengupta that the assumption NP has small circuits collapses
PH to ${\rm S}_2^p$
becomes the strongest version to date of the Karp-Lipton Theorem.

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