On the Power of Probabilistic Choice in Synchronous Parallel Computations

This paper introduces probabilistic choice to synchronous parallel machine models; in particular parallel RAMs. The power of probabilistic choice in parallel computations is illustrated by parallelizing some known probabilistic sequential algorithms. We characterize the computational complexity of time, space, and processor bounded probabilistic prallel RAMs in terms of the computational complexity of probabilistic sequential RAMs. We show that parallelism uniformly speeds up time bounded probabilistic sequential RAM computations by nearly a quadratic factor. We also show that probabilistic choice can be, eliminated from parallel computations by introducing nonuniformity.

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