A Probabilistic-Time Hierarchy Theorem for “Slightly Non-uniform” Algorithms
Unlike other complexity measures such as deterministic and nondeterministic time and space, and non-uniform size, it is not known whether probabilistic time has a strict hierarchy. For example, as far as we know it may be that BPP is contained in the class BPtime(n). In fact, it may even be that the class BPtime(nlogn) is contained in the class BPtime(n).
We also discuss conditions under which a hierarchy theorem can be proven for fully uniform Turing machines. In particular we observe that such a theorem does hold if BPP has a complete problem.
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