The Global Power of Additional Queries to Random Oracles

Abstract It is shown that, for every k ≥ 0 and every fixed algorithmically random language B, there is a language that is polynomial-time, 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.

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