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Hierarchies for semantic classes

Published:22 May 2005Publication History

ABSTRACT

We show that for any constant a, ZPP/b(n) strictly contains ZPTIME(na)/b(n) for some b(n) = O(log n log log n). Our techniques are very general and give the same hierarchy for all common semantic time classes including RTIME, NTIME ∩ coNTIME, UTIME, MATIME, AMTIME and BQTIME.We show a stronger hierarchy for RTIME: For every constant c, RP/1 is not contained in RTIME(nc)/(log n)1/2c. To prove this result we first prove a similar statement for NP by building on Zák's proof of the nondeterministic time hierarchy.

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        cover image ACM Conferences
        STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
        May 2005
        778 pages
        ISBN:1581139608
        DOI:10.1145/1060590

        Copyright © 2005 ACM

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        • Published: 22 May 2005

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