Limits on the power of concurrent-write parallel machines

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Abstract

The computation of specific functions using the most general form of concurrent-read-concurrent-write parallel RAM is considered. It is shown that such a machine can compute any function of Boolean inputs in time log n − log log n + O(1) given a polynomial number of processors and memory cells and that this bound is tight for integer addition. Despite this evidence of the power of the model we show that a very simple function, namely parity, requires time Ω (log n) to compute given a polynomial bound on the number of processors, independent of the number of memory cells.

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This work was done while the author was at the University of Toronto.

Current address: Department of Computer Science, FR-35, University of Washington, Seattle, Washington 98195.