A note on zero error algorithms having oracle access to one NP query

  • Authors:

  • Jin-Yi Cai;Venkatesan T. Chakaravarthy

  • Affiliations:

  • Computer Science Department, Univ. of Wisconsin, Madison, WI;IBM India Research Lab, IIT Campus, New Delhi, India

  • Venue:
  • COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
  • Year:
  • 2005

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Abstract

It is known that ${{\rm S}_2^p} \subseteq {{{\rm ZPP}}^{{\rm NP}}}$ [3]. The reverse direction of whether ZPPNP is contained in S$_{\rm 2}^{p}$ remains open. We show that if the zero-error algorithm is allowed to ask only one query to the NP oracle (for any input and random string), then it can be simulated in S$_{\rm 2}^{p}$. That is, we prove that ${{{\rm ZPP}}^{{\rm NP}[1]}} \subseteq {{\rm S}_2^p}$.