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Simplicity, relativizations and nondeterminism. (English) Zbl 0567.68027
Relativizations of complexity classes in which simple sets exist are considered. A recursive oracle is constructed relative to which a simple set exists for NP. Some other general theorems are proven, showing that the time bounds are not a crucial hypothesis; bounds on the way in which the oracle is accessible, namely, the number of queries and/or the number of nondeterministic steps, are shown to be the fundamental hypothesis. As a result, simple sets are shown to exist in many different relativized complexity classes.

68Q25 Analysis of algorithms and problem complexity
03D15 Complexity of computation (including implicit computational complexity)
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