On the Power of reading and writing simultaneously in parallel computations
In the standard model of Cook, Dwork, and Reischuk  for the derivation of lower bounds, one computation step of a CREW-PRAM consists of a read phase, internal computation, and a write phase. We investigate the case when one step comprises only internal computation and one communication phase instead of two, but we have either reading or writing and internal computation, and thus allow the mixed occurrence of reading and writing (of different memory cells) at the same time. We show that simultaneous reading and writing saves communication phases. In detail, we show that the computation of the OR-function requires exactly log n “single communication” steps instead of 0.72 log n “double communication” steps on the standard model. We provide a general lower bound of log(deg(f)) in terms of the degree of a function f. We obtain a lower bound of 0.76 log n for the computation of critical functions and present a critical function that can be computed in 0.90 log n steps. Finally we demonstrate a tight correspondence between CROW-PRAM's of the modified form and the decision tree complexity.
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