For a next seminar of the proofs and algorithms pole of LIX, we are happy to welcome Giuseppe Di Molfetta.

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.

Link to the online conference

The list of next seminars can be found at: https://smimram.gitlabpages.inria.fr/proofs-algorithms/seminar/

The calendar of seminars can be found at: https://smimram.gitlabpages.inria.fr/proofs-algorithms/seminar.ics