Multi-limited Lindenmayer Systems

The theory of L systems originated with the biologist and mathematician Aristide Lindenmayer. His original goal was to provide mathematical models for the simultaneous development of cells in filamentous organisms. Since L systems may be viewed as rewriting systems, their generated languages, i.e., sets of organisms encoded by strings, are also subject to formal language theory, which aims to classify formal languages as well as their generating mechanisms according to various properties, such as generative power, decidability, etc. D. Wätjen introduced and studied k-limited L systems in order to combine the purely sequential mode of rewriting and the purely parallel mode of rewriting in context-free grammars, respectively, L systems. In biology, these systems may be interpreted as organisms, for which the simultaneous growth of cells is restricted by the supply of some resources of food being limited by some finite value k. In this thesis the constraint of a common limit k is relaxed in favor of individual resource limits κ(a) for every cell-type a, which yields the new notion of multilimited L system. The language families generated by such systems are then classified according to their sets of limits κ(a). At first, an intuitive approach to the different mechanisms of the L system variants is provided by presenting a method for the graphical interpretation of L systems, the so-called turtle interpretation. Suitable computer programs implementing a turtle interpreter as well as free-programmable simulators for multi-limited, k-limited, and uniformly k-limited L systems, are developed and their source-code is appended. After this outline of an application area of L systems outside formal language theory, multi-limited L systems are investigated under aspects of formal language theory. Their generated language families are compared to each other, to Wätjen’s k-limited as well as to non-limited language families, and to the families of the Chomsky Hier-