A probabilistic relation between desirable and feasible, models of parallel computation

We present a powerful probabilistic technique for simulating strong models of synchronized parallel computation by weaker ones. The technique is demonstrated by an algorithm simulating an <italic>n</italic> processor PRAM, with an arbitrary large shared memory, by an <italic>n</italic> processor ULRTACOMPUTER (a set of <italic>n</italic> processors communicating through a bounded degree network, and sharing no common memory). We prove that if a program required <italic>t</italic> PRAM steps, our simulation algorithm executes it on the ULTRACOMPUTER within <italic>O</italic>(<italic>t</italic>log<supscrpt>2</supscrpt><italic>n</italic>) steps with overwhelming probability.