This paper gives a full characterization of the time needed to compute a boolean function on a CREW PRAM with an unlimited number of processors. The characterization is given in terms of a new complexity measure of boolean functions: the "block sensitivity". This measure is a generalization of the well know "critical sensitivity" measure (see [wl, [CDR], [Si]). The block sensitivity is also shown to relate to the boolean decision tree complexity, and the implication is that the decision tree

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... plexity also fully characterizes the CREW PRAM complexity. This solves an open problem of w]. Our results imply that changes in the instruction set of the processors or in the capacity of the shared memory cells do not change by more than a constant factor the time required by a CREW PRAM to compute any boolean function. Moreover, we