S^p _2 \subseteq ZPP^{NP}

  • Authors:

  • J. Cai

  • Affiliations:

  • -

  • Venue:
  • FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
  • Year:
  • 2001

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Abstract

We show that the class S_2^p is a subclass of ZPPNP. 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 S_2^p becomes the strongest version to date of the Karp-Lipton Theorem. We also discuss the problem of finding irrefutable proofs for S_2^p in ZPPNP.