Efficient simulations between concurrent-read concurrent-write pram models

We give several simple and efficient algorithms: for simulations of stronger GROW PRAMs on weaker ones. The models that we consider are the well-known PRIORITY, ARBITRARY and COMMON PRAMs, and COLLISION and COLLISION⁺, defined by the property that a special collision symbol is stored in each memory cell into which more than one processor attempts to write, or more than one value is attempted to be written, respectively, in a given step. Our results are the following, where n denotes the number of processors of the simulated PRAM: 1) A O(1)-time simulation between any pair of models, provided that the simulating machine has O(n log n) processors; 2) Two n-processor simulations: of PRIORITY on ARBITRARY with O(loglog n) slowdown, and of PRIORITY on COLLISION⁺ with 2 O((loglog n)²) slowdown.