On the membership question in some Lindenmayer-systems

Abstract

Lindenmayer-systems are a family of string-generating systems, and several types can be distinguished, of different strength. The subject of this article is the membership question in the languages generated by determinate, no-input Lindenmayer-systems (or, shortly, D0L-languages). For propagating D0L-systems (which contain no production rules yielding the empty string) the question is easily answered. For D0L-systems in general it can be solved in two steps, involving the construction of an intermediate “backbone” system, which is propagating.