Cellular Automata and Discrete Complex Systems

Invertible transducers are Mealy automata that determine injective maps on Cantor space and afford compact descriptions of their associated transduction semigroups and groups. A lot of information has been unearthed in the last two decades about algebraic aspects of these machines, but relatively little is known about their automata-theoretic properties and the numerous computational problems associated with them. For example, it is quite difficult to pin down the computational complexity of the orbits of maps defined by invertible transducers. We study some of these properties in the context of socalled m-lattices, where the corresponding transduction semigroup is a free Abelian group of finite rank. In particular we show that it is decidable whether an invertible transducer belongs to this class. Propagation, Diffusion and Randomization in Cellular Automata