ADAPTIVE LOGSPACE REDUCIBILITY AND PARALLEL TIME

We discuss two notions of functional oracle for logarithmic space-boun ded machines, which differ in whether there is only one oracle tape fo r both the query and the answer or a separate tape for the answer, whi ch can still be read while the next query is already being constructed . The first notion turns out to be basically nonadaptive, behaving lik e access to an oracle set. The second notion, on the other hand, is ad aptive. By imposing appropriate bounds on the number of functional ora cle queries made in this computation model, We obtain new characteriza tions of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characteri zation of parallel classes, we solve open questions of Wilson.