Codes defined by multiple sets of trajectories

We investigate the use of shuffle on trajectories to model certain classes of languages arising in the theory of codes. In particular, for each finite set of sets of trajectories, which we call a hyperset of trajectories, we define a class of languages induced by that hyperset of trajectories. We investigate the properties of hypersets of trajectories and the associated classes of languages, including the problem of decidability of membership and the problem of equivalence of hypersets of trajectories.