Dynamic Parallel Complexity of Computational Circuits

Gary L. Miller, Shang-Hua Teng

Abstract: The dynamic parallel complexity of general computational circuits (defined in introduction) is discussed. We exhibit some relationships between parallel circuit evaluation and some uniform closure properties of a certain class of unary functions and present a systematic method for the design of processor efficient parallel algorithms for circuit evaluation. Using this method: (1) we improve the algorithm for parallel Boolean circuit evaluation; (2) we give a nontrivial upper bound for parallel min-max-plus circuit evaluation; (3) we partially answer the first open question raised in [MiRK85] by showing that all circuits over finite noncommutative semi-ring and circuits over infinite non-commutative semi-ring which has finite dimension over a commutative semi-ring can be evaluated in polylogarithmic time in its size and degree using M(n) processors. Moreover, we develop a theory for determining closure properties of certain classes of unary functions.