Stable String Languages of Lindenmayer Systems

The stable string operation selects from the strings produced by a rewriting system those strings which are invariant under the rewriting rules. Stable string languages of Lindenmayer systems are investigated. (Lindenmayer systems are a class of parallel rewriting systems originally introduced to model the growth and development of filamentous organisms.) For families of Lindenmayer systems the sets of languages obtained by the stable string operation are shown to coincide with the sets of languages obtained from these systems by intersecting the languages they produce with a terminal alphabet, except in the case of Lindenmayer systems without interactions. The equivalence of a biologically highly relevant notion, i.e., that of equilibrium oriented behavior in models of morphogenesis, and the formal language concept of intersection with a terminal alphabet, establishes a new link between formal language theory and theoretical biology. Relevance to these two fields is briefly discussed.