On Adaptive DLOGTIME and POLYLOGTIME Reductions

We investigate properties of the relativized NC and AC hierarchies in their DLOGTIME-, respectively, ALOGTIME-uniform setting and show that these hierarchies can be characterized in terms of adaptive reducibility in deterministic (poly)logarithmic time, i.e. in time O(log n)i for i≥0. Using this characterization, we substantially generalize various previous results concerning the structure of the NC and AC hierarchies.

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