Optimal Separation of EROW and CROWPRAMs

We consider the problem of evaluating a Boolean function on PRAMs. We exhibit a Boolean function f : {0, 1} → {0, 1} that can be evaluated in time O(log log n) on a deterministic CROW (Concurrent Read Owner Write) PRAM, but requires time Ω(log n) on EROW (Exclusive Read Owner Write) PRAMs. Our lower bound also holds for randomized Monte Carlo EROW PRAMs. This Boolean function is derived from the well-known pointer chasing problem, and was first defined by Nisan and Bar-Yossef [11]. Our lower bound improves a special case of the previous result of Nisan and Bar-Yossef, who proved Ω( √ log n) lower bound for this function on deterministic EREW PRAMs (and hence for EROW PRAMs). Our result is the first to achieve the best possible separation between the computational power of CROW and EROW PRAMs for functions on complete domains (Boolean or non-Boolean), improving previous results [7, 6, 11].