Effective Parallelism Rate by Reversible PCA Dynamics
Résumé
Probabilistic Cellular Automata generalise CA by implementing an updating rule defined through a probability. It means a synchronous updating of the constituting cells/sites’ states is possible. PCA differ from the interacting particle systems where in general at most one site is possibly updated at a time. For a family of reversible (in a stochastic sense) PCA dynamics, we study through numerical simulations the effective flips occurring. When infinitely many sites are considered, there are two regime: an ergodic one and a phase transition regime. When finitely many interacting sites are considered, these regimes corresponds to very different effective parallelism rate. We quantify these changes. When phase transition holds, PCA dynamics is in fact an α-asynchronous one.