In symbolic dynamics we study discrete dynamical systems whose states are given by a spatial arrangement of symbols from a finite alphabet. Such systems on the one hand occur as models in biology, traffic modelling or the study of quasicrystals. On the other hand, they can be used to approximate dynamical systems with a continuous state space. Additionally, they also found applications in various areas of pure mathematics such as geometric group theory or number theory.

Our main focus here is on classification problems. We try to answer  the question, under which conditions two symbolic dynamical systems can be transformed into each other in a structure preserving way. In particular we explore topological conjugacies between cellular automata and subshifts of finite type.