Lower bounds with smaller domain size on concurrent write parallel machines

The author proves an optimum lower bound, separating the PRIORITY and the COMMON PRAM models on a much more reasonably sized input domain than that shown by R.B. Boppana (1989). The proposed techniques provide a greater understanding of the partial information a processor learns about the input. For example, the author defines a new measure of the dependency that a function has on a variable and develops new set theoretic techniques to replace the use of Ramsey theory (which had forced the domain size to be large).<>