Hierarchy Theorems for Probabilistic Polynomial Time

Authors:
Lance Fortnow;Rahul Santhanam
Affiliations:
University of Chicago;University of Chicago
Venue:
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Year:
2004

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Abstract

We show a hierarchy for probabilistic time with one bit of advice, specifically we show that for all real numbers 1 驴驴 0, there is a language L computable on average in BPP but not on average in BPTIME(n^(d)). We build on Barak's techniques by using a different translation argument and by a careful application of the fact that there is a PSPACE-complete problem L such that worst-case probablistic algorithms for L take only slightly more time thane average-case algorithms.