Substitutions, Trajectories and Noisy Channels

The word substitutions are binary word operations which can be basically interpreted as a deletion followed by insertion, with some restrictions applied. Besides being itself an interesting topic in formal language theory, they have been naturally applied to modelling noisy channels. We introduce the concept of substitution on trajectories which generalizes a class of substitution operations. Within this framework, we study their closure properties and decision questions related to language equations. We also discuss applications of substitution on trajectories in modelling complex channels and a cryptanalysis problem.