Abstract
We discuss two notions of functional oracle for logarithmic space-bounded machines, which differ in whether there is only one oracle tape for both the query and the answer or a separate tape for the answer, which can still be read on while the next query is already being constructed. The first notion turns out to be basically non-adaptive, behaving like access to an oracle set. The second notion, on the other hand, is adaptive. By imposing appropriate bounds on the number of functional oracle queries made in this computation model, we obtain new characterizations of the NC and AC hierarchies; thus the number of oracle queries can be considered as a measure of parallel time. Using this characterization of parallel classes, we solve open questions of Wilson.
(Conference Abstract)
Work partially supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).
Work done while visiting the L.S.I. Department of UPC in Barcelona supported by Deutsche Forschungsgemeinschaft (DFG-Forschungsstipendium Je 154/1-1). Final version partially supported by DFG-SFB 342, subproject A4.
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Àlvarez, C., Balcázar, J.L., Jenner, B. (1991). Functional oracle queries as a measure of parallel time. In: Choffrut, C., Jantzen, M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020817
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DOI: https://doi.org/10.1007/BFb0020817
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