On Accepting Pure Lindenmayer Systems

Abstract

We consider pure Lindenmayer systems, more precisely, 0L and T0L systems as language accepting devices and compare them to their generating counterparts. Accepting Lindenmayer systems can be seen as systems of inverse finite substitutions which are iteratively applied over a free monoid. Hereby, we investigate the deterministic case in detail, comparing several different concepts of determinism in such systems. Whereas in the usual generating case these concepts trivially are equally powerful, the structure of families of accepted languages is much richer. In passing, the case of unary Lindenmayer systems is investigated.