On the Bpp Hierarchy Problem
نویسنده
چکیده
In this paper we give arguments both for and against the existence of an oracle A, relative to which BPP equals probabilistic linear time. First, we prove a structure theorem for probabilistic oracle machines, which says that either we can x the output of the machine by setting the answer to only polynomially many oracle strings, or else we can set part of the oracle such that the machine becomes improper. This theorem could help complete the construction of the oracle A, which was proposed by Fortnow and Sipser in 2]. Second, we show that there are previously unknown problems with this construction. Thus the question whether probabilistic polynomial time has a hierarchy relative to all oracles remains completely open.
منابع مشابه
The University of Chicago Hierarchy Theorems and Resource Tradeoffs for Semantic Classes a Dissertation Submitted to the Faculty of the Division of the Physical Sciences in Candidacy for the Degree of Doctor of Philosophy Department of Computer Science By
Computational complexity theory studies the minimum resources (time, space, randomness etc.) to solve computational problems. Two fundamental questions in this area are: 1. Can more problems be solved given more of a given resource? A positive answer to this question is known as a hierarchy theorem. 2. Can one resource be traded off with another when solving a given problem? Such a result is kn...
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