Optimal separation of EROW and CROW PRAMs

We consider the problem of evaluating a Boolean function on PRAMs. We exhibit a Boolean function f:{0,1}ⁿ→{0,1} that can be evaluated in time O(log log n) in a deterministic CROW (concurrent read owner write) PRAM model, but requires time Ω(log n) in EROW (exclusive read owner write) PRAM. Our lower bound also holds in the randomized Monte Carlo EROW model. This Boolean function is derived from the well-known pointer chasing problem, and was first considered by Nisan and Bar-Yossef (1997). Our lower bound improves a special case of the previous result of Nisan and Bar-Yossef, who proved a lower bound of Ω(√(log n)) for this function in the deterministic EREW model (and hence in the EROW model). Our result is the first to achieve the best possible separation between the CROW and EROW PRAM models for functions on complete domains (Boolean or nonBoolean), improving the previous results (E. Gafni et al., 1989; F. Fich et al., 1990; N. Nisan et al., 1997).