Words and Bisimulations of Dynamical Systems

In this paper we study bisimulations on dynamical systems through a given partition. Our aim is to give a new vision of the notion of bisimulation by using words. To achieve this goal, we encode the trajectories of the transition system as words. This method was introduced in our paper “On o-minimal hybrid systems” in order to give a new proof of the existence of a finite bisimulation for o-minimal hybrid systems (as previously proved in a paper by Lafferriere G., Pappas G.J. and Sastry S.). Here we want to provide a systematic study of this method in order to obtain a procedure for building finite bisimulations based on words.