Laboratoire d'Informatique de Grenoble

Abstract: Cellular Automata constitute the most established distributed model of computation on space-time grid. It is clearly physics-like, in the sense that it shares some fundamental symmetries such as homogeneity (invariance of the physical laws in time and space), causality, and often reversibility. When a CA is invariant under a transformation identically performed at every point of the configuration space, they are said to have a global symmetry. Typical global symmetries include reflections, rotations, time inversion. Local symmetries, the cornerstone of gauge theories, is a stronger constraint. I will provide a constructive method, a step-by-step procedure, to make cellular automata invariant under the local action of a gauge group and the notion of gauge-equivalence will be formalized. Then, I will extend such results into the Quantum realm by means of a concrete example. In conclusion, I will discuss how such discrete time and discrete space gauge invariant automata can be described at larger scale, e.g. by differential equations, with and without information loss.