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 implementa¬tions 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.