The Random Oracle Hypothesis is False (1994)
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| Venue: | Journal of Computer and System Sciences |
| Citations: | 24 - 2 self |
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@TECHREPORT{Chang94therandom,
author = {Richard Chang and Benny Chor and Oded Goldreich and Juris Hartmanis and Johan Hastad and Desh Ranjan and Pankaj Rohatgi},
title = {The Random Oracle Hypothesis is False},
institution = {Journal of Computer and System Sciences},
year = {1994}
}
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Abstract
The Random Oracle Hypothesis, attributed to Bennett and Gill, essentially states that the relationships between complexity classes which hold for almost all relativized worlds must also hold in the unrelativized case. Although this paper is not the first to provide a counterexample to the Random Oracle Hypothesis, it does provide a most compelling counterexample by showing that for almost all oracles A, IP A 6= PSPACE A . If the Random Oracle Hypothesis were true, it would contradict Shamir's result that IP = PSPACE. In fact, it is shown that for almost all oracles A, co-NP A 6` IP A . These results extend to the multi-prover proof systems of Ben-Or, Goldwasser, Kilian and Wigderson. In addition, this paper shows that the Random Oracle Hypothesis is sensitive to small changes in the definition. A class IPP, similar to IP, is defined. Surprisingly, the IPP = PSPACE result holds for all oracle worlds. 1 Department of Computer Science, Cornell University, Ithaca, NY 14853, U.S.A...
