On the complexity of nonuniform wavelength-based machine

The wavelength-based machine, or simply w -machine, is an optical computational model, which is designed based on simultaneous movement of several wavelengths in a single light ray, and simultaneous effect of simple optical devices on them. In this paper, we investigate nonuniform complexity classes of w -machine, based on three complexity measures, namely, size, time, and word length. We show that the class of languages which can be generated by constant size nonuniform w -machines contain infinitely many Turing undecidable languages. Also, we show that polynomial size nonuniform w -machines generate all NP languages, and every NP-hard language requires at least polynomial time and polynomial size nonuniform w -machines to be generated. We prove that the class of languages which can be generated by polynomial size nonuniform w -machines is equal to NP/poly, and almost all languages require exponential size and polynomial time nonuniform w -machines to be generated.