Dynamics of Discrete Event Systems

We provide a mathematical framework for the analysis of discrete dynamical systems. These are systems with a discrete state spaces. We find that Hilbert spaces are the appropriate spaces in which to embed the dynamics. In this formulation, it is possible to define and write equations of motion for the system. Although Hilbert spaces are generally associated with quantum systems in physics, they are employed here in a purely classical manner; both dynamical evolution and results of measurements are just as in classical mechanics. Two examples analysed are Euclid''s algorithm and the Turing machine.