Continuous-space model of computation is Turing universal
Thomas J. Naughton · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
Our model of computation (theoretical machine) was designed for the analysis of analog Fourier optical processors, its basic data unit being a continuous image of unbounded resolution. In this paper, we demonstrate the universality of our machine by presenting a framework for arbitrary Turing machine simulation. Computational complexity benefits are also demonstrated by providing a O(log2n) algorithm for a search problem that has a lower bound of n - 1 on a Turing machine.