On bonded sequential and parallel insertion systems

We introduce a new variant of insertion systems, namely bonded insertion systems. In such systems, words are not only formed by usual letters but also by bonds between letters. Words which can be inserted, have “free” bonds at their ends which control at which positions in a word they can be inserted (namely only there, where the bonds “fit”). Two kinds of bonded insertion systems are defined in this paper: so-called bonded sequential insertion systems and bonded parallel insertion systems. In a sequential system, there is only one word inserted at a time. In a parallel system, there is a word inserted at every possible position in parallel in one time step. We investigate the generative capacity of those two kinds and relate the families of generated languages to some families of the Chomsky hierarchy and to families of languages generated by Lindenmayer systems. Additionally, we investigate some closure properties.