Relativized collapsing between BPP and PH under stringent oracle access

Authors:
Jin-Yi Cai;Osamu Watanabe
Affiliations:
Computer Sciences Department, University of Wisconsin, Madison, WI;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
Venue:
Information Processing Letters
Year:
2004

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Abstract

We propose a new model of stringent oracle access defined for a general complexity class. For example, when comparing the power of two machine models relative to some oracle set X, we restrict that machines of both types ask queries from the same segment of the set X. In particular, for investigating polynomial-time (or polynomial-size) computability, we propose polynomial stringency, bounding query length to any fixed polynomial of input length. Under such stringent oracle access, we show an oracle G such that BPPG = PHG.