Abstract

There is much interest in recent literature in employing symbolic substitution (SS) for general-purpose digital optical computing. We evaluate and compare the SS with the programmable optoelectronic multiprocessors (POEMs) paradigms currently under development at UCSD. First, we discovered that the computational ability of an optical SS system (without straightforward global interconnect) is essentially equivalent to a 2-D VLSI SIMD mesh connected array of small-grain processors. We can show that a SS rule can be simulated by a mesh of electronic processors using only a small number of cycles depending on the complexity of the rule. In addition, the simulation of even a very small-grain processor mesh in SS seems to require more space and time. Furthermore, SS lacks any means of implementing a RAM function because of its local interconnection topology. This implies that space–time trade-offs are hard to achieve on SS machines. On the other hand, the POEMs paradigm can implement any variation of the three parameters used to classify parallel systems: synchrony (SIMD or MIMD); topology (local or global); and granularity (small or large grain). By mapping commonly used algorithms such as FFT, sorting, and graph optimization onto a SS and POEMs architectures with global interconnection topology (e.g., hypercube), we determined that the SS approach (operated at very high clock rates, e.g., above 500 MHz) is outperformed by the POEMs (operated at much slower clock rates, e.g., 10 MHz). Therefore, the speed of the devices used in SS systems is offset by the inefficiency of the algorithms used on a locally interconnected topology.

© 1988 Optical Society of America