Routing, merging, and sorting on parallel models of computation
Journal of Computer and System Sciences
Deterministic selection in O(loglog N) parallel time
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Upper and lower time bounds for parallel random access machines without simultaneous writes
SIAM Journal on Computing
Log-logarithmic selection resolution protocols in a multiple access channel
SIAM Journal on Computing
Relations between concurrent-write models of parallel computation
SIAM Journal on Computing
The parallel complexity of element distinctness is Ω(√log n)
SIAM Journal on Discrete Mathematics
On the power of concurrent-write PRAMs with read-only memory
Information and Computation
Optimal separations between concurrent-write parallel machines
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On separating the EREW and CREW PRAM models
Theoretical Computer Science
Every robust CRCW PRAM can efficiently simulate a PRIORITY PRAM
SPAA '90 Proceedings of the second annual ACM symposium on Parallel algorithms and architectures
Processor-time tradeoffs in PRAM simulations
Journal of Computer and System Sciences
Fast and efficient simulations among CRCW PRAMs
Journal of Parallel and Distributed Computing
Separating the power of EREW and CREW PRAMs with small communication width
Information and Computation
Efficient Simulations Between Concurrent-Read Concurrent-Write PRAM Models
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Fast and Optimal Simulations between CRCW PRAMs
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
New Simulations between CRCW PRAMs
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
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It is known that Θ(log n/log log n) steps are needed to simulate one step of ARBITRARY CRCW PRAMs by COMMON CRCW PRAMs, but it was open whether there is a faster simulation when randomization is allowed. This paper gives both positive and negative answers. (i) It is shown that one step of ARBITRARY can be simulated by O(log m/k(log log m-log k) + log log n) steps on randomized COMMON with error-rate n-c, where m = n/k is the number of different memory cells into which at least one processor of the simulated PRAM attempts to write. The deterministic Θ(log n/log log n)-step simulation does not become faster for smaller m, while our randomized simulation becomes O(log log n) when m≤n log log n/log n. (ii) It is shown that when m = n, Ω(log n/log log n) steps are needed to simulate one step of ARBITRARY by COMMON even if randomization is allowed. This lower-bound result needs some assumption on processor communication but it strongly suggests randomization does not help when m is small.