The Global Power of Additional Queries to Random Oracles
| Citations: | 8 - 1 self |
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@MISC{Book_theglobal,
author = {Ronald V. Book and Jack H. Lutz and David M. Martin},
title = {The Global Power of Additional Queries to Random Oracles},
year = {}
}
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Abstract
. It is shown that, for every k 0 and every fixed algorithmically random language B, there is a language that is polynomialtime, truth-table reducible in k + 1 queries to B but not truth-table reducible in k queries in any amount of time to any algorithmically random language C. In particular, this yields the separation Pk-tt(RAND) $ P (k+1)-tt (RAND), where RAND is the set of all algorithmically random languages. 1 Introduction Will an algorithm have increased computational power when it is modified to be able to ask additional questions? One way of making this question precise is to consider it in the context of reducibilities computed by algorithms with bounds on their computational resources. In this paper, we investigate the phenomenon of increased access to oracle sets lending increased computational power for bounded truth-table reducibilities computed in polynomial time. We show that, in a strong global sense, if just one more question can be asked of sets with "maximum info...
