L Systems

L systems are parallel rewriting systems which were originally introduced in 1968 to model the development of multicellular organisms, [L1]. The basic ideas gave rise to an abundance of language-theoretic problems, both mathematically challenging and interesting from the point of view of diverse applications. After an exceptionally vigorous initial research period (roughly up to 1975; in the book [RSed2], published in 1985, the period up to 1975 is referred to, [RS2], as \when L was young"), some of the resulting language families, notably the families of D0L, 0L, DT0L, E0L and ET0L languages, had emerged as fundamental ones in the parallel or L hierarchy. Indeed, nowadays the fundamental L families constitute a similar testing ground as the Chomsky hierarchy when new devices (grammars, automata, etc.) and new phenomena are investigated in language theory. L systems were introduced by Aristid Lindenmayer in 1968, [L1]. The original purpose was to model the development of simple lamentous organisms. The development happens in parallel everywhere in the organism. Therefore, parallelism is a built-in characteristic of L-systems. This means, from the point of view of rewriting, that everything has to be rewritten at each step of the rewriting process. This is to be contrasted to the \sequential" rewriting of phrase structure grammars: only a speci c part of the word under scan is rewritten at each step. Of course, the e ect of parallelism can be reached by several se-