Section: New Results

Causal Graph Dynamics

• Participants: Pablo Arrighi, Simon Martiel, Simon Perdrix.

Causal Graph Dynamics extend Cellular Automata to arbitrary time-varying graphs of bounded degree. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of symmetries: shift-invariance (it acts everywhere the same) and causality (information has a bounded speed of propagation). Pablo Arrighi (LIS, Marseille), Simon Martiel (Atos-Bull) and Simon Perdrix have considered a natural physics-like symmetry, namely reversibility. In particular, they extended two fundamental results on reversible cellular automata, by proving that the inverse of a causal graph dynamics is a causal graph dynamics, and that these reversible causal graph dynamics can be represented as finite-depth circuits of local reversible gates. These results have been published in the journal Natural Computing [16].