A zero-one law for RP and derandomization of AM if NP is not small

Authors:
Russell Impagliazzo;Philippe Moser
Affiliations:
Computer Science and Engineering Department UC, San Diego, USA;Department of Computer Science, National University of Ireland, Maynooth Co. Kildare, Ireland
Venue:
Information and Computation
Year:
2009

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Abstract

We show that if RP does not have p-measure zero then ZPP = EXP. As corollaries we obtain a zero-one law for RP in EXP, and that both probabilistic classes ZPP and RP have the same measure in EXP. We also prove that if NP does not have p-measure zero then NP = AM.