Discrete Signal Machine via Pretopology - one step from signal machines to cellular automata
Abstract
Signal machines are a model of computation with continuous space and time, generalizing discrete signals in cellular automata on an euclidean plane. In this paper, we define discrete signal machines which purpose is to discretize continuous space-time diagram of signal machines into signals and collisions rules in the discrete space-time Z×N by using notions of pretopology, a theory generalizing classical topology. The result is a definition of discrete signals and collisions based on neighborhoods in a pretopological space. It is a first step to obtain automatically cellular automata from signal machines.