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Relativized Worlds without Worst-Case to Average-Case Reductions for NP

Published:01 September 2012Publication History
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Abstract

We prove that, relative to an oracle, there is no worst-case to average-case reduction for NP. We also handle classes that are somewhat larger than NP, as well as worst-case to errorless-average-case reductions. In fact, we prove that relative to an oracle, there is no worst-case to errorless-average-case reduction from NP to BPPNP. We also handle reductions from NP to the polynomial-time hierarchy and beyond, under strong restrictions on the number of queries the reductions can make.

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    • Published in

      cover image ACM Transactions on Computation Theory
      ACM Transactions on Computation Theory  Volume 4, Issue 3
      September 2012
      46 pages
      ISSN:1942-3454
      EISSN:1942-3462
      DOI:10.1145/2355580
      Issue’s Table of Contents

      Copyright © 2012 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 1 September 2012
      • Accepted: 1 June 2012
      • Revised: 1 January 2012
      • Received: 1 July 2011
      Published in toct Volume 4, Issue 3

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