Models of parallel computation and optical computing

Abstract

Theoretical models of computation (automata, Turing machines, random access machines, etc.) define not only what is computable but determine how much time and/or space is required for a computation. The parallel extensions of the sequential models usually offer significant speedup in algorithm execution (not all algorithms can be parallelized, however). Real parallel computer architectures based on these parallel computation models should exhibit the same algorithmic speedup. A complexity hierarchy can be defined for parallel computation models based on the space and/or time speedup of certain classes of algorithms. In particular the parallel shared memory models1 are some of the more powerful of the parallel computation models. Their close resemblance to actual computer architectures provide guidance for real architectural design and their massive interconnection requirements are well suited for implementation in optical computing architectures. In addition, the shared memory models have recently been shown to simulate deterministic Boltzmann machines and threshold-logic Turing machines. Thus optical machines based on these parallel models can potentially exhibit the computational power of the shared memory models. These parallel computation models and their implications for optical computing are discussed.