Non-Determinism in Lindenmayer Systems and Global Transformations

Global transformations provide a categorical framework for capturing synchronous rewriting systems, generalizing cellular automata to dynamical systems over dynamic spaces. Originally developed for addressing deterministic dynamical systems, the presented work raises the question of non-determinism. While a usual approach is to develop a general non-deterministic setting where deterministic systems can be retrieved as a specific case, we show here that by choosing the right parametrization, global transformations can already be used to handle non-determinism. Context-free Lindenmayer systems, already shown to be captured by global transformation in the deterministic case, are used to illustrate the approach. From this concrete example, the formal obstructions are exhibited, leading to a solution involving a 2-categorical monad and its associated Kleisli construction