A complexity theory for unbounded fan-in parallelism

Abstract

A complexity theory for unbounded fan-in parallelism is developed where the complexity measure is the simultaneous measure (number of processors, parallel time). Two models of unbounded fan-in parallelism are (1) parallel random access machines that allow simultaneous reading from or writing to the same common memory location, and (2) circuits containing AND's, OR's and NOT's with no bound placed on the fan-in of gates. It is shown that these models can simulate one another with the number of processors preserved to within a polynomial and parallel time preserved to within a constant factor. Reducibilities that preserve the measure in this sense are defined and several reducibilities and equivalences among problems are given. New upper bounds on the (unbounded fan-in) circuit complexity of symmetric Boolean functions are proved.