Complexity analysis of optical-computing paradigms.

Optical computing has been suggested as a means of achieving a high degree of parallelism for both scientific and symbolic applications. While a number of implementations of logic operations have been forwarded, all have some characteristic that prevents their direct extension to functions of a large number of input bits. We analyze several of these implementations and demonstrate that all these implementations require that some measure of the system (area, space-bandwidth product, or time) grow exponentially with the number of inputs. We then suggest an implementation whose complexity is no greater than the best theoretical realization of a Boolean function. We demonstrate the optimality of that realization, to within a constant multiple, for digital optical-computing systems realized by bulk spatially variant elements.