Complexity of optical computing paradigms: Computational implications and a suggested improvement

Abstract

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 which prevents their direct extension to functions of a large number of input bits. This paper will analyze several of these implementations and demonstrate that all these implementations require some measure of the system (area, space-bandwidth product, or time) to grow exponentially with the number of inputs. We will then suggest an implementation whose complexity is not greater than the best theoretical realization of a boolean function. We will demonstrate the optimality of the realization, to within a constant multiple, for digital optical computing systems realized by bulk space-variant elements.