Parentheses Grammars and Lindenmayer Grammars

The pioneering research of Lindenmayer and his co-workers on what are now called OL-systems has yield a rich mathematical theory for modeling the development of organism without cellular interaction. Concrete examples of the biological relevance of the theory of OL-systems can be found in some of the earliest literature on the subject. [L1] Yet, cellular interaction seems to be necessary for some types of development. Various extensions of the OL-systems, yield systems with provably stronger generative power. A general model for modeling cellular interaction was introduced by Lindenmayer very early in the history of L-systems. [L2] This led to a search for models with more limited types of interaction. One of the most studied of these models is the ETOL-system introduced by Rozenberg [R1, R2]