ON THE NUMBER OF ACTIVE SYMBOLS IN LINDENMAYER SYSTEMS
A symbol a is called active in an L system G if there is a rule a -> v with a 6 not equal v in some table of G. By Ac(X)(L) we denote the number of active symbols necessary to generate L by L systems of type X. For two types X and Y of L systems such that the corresponding languages families L (X) and L (Y) satisfy L (X) subset of L (Y), we say that Y is more efficient than X, if there is a sequence of languages L(n) is an element of L (X), n >= 1, such that Ac(X)(L(n)) >= n and AcY (L(n)) <= k for some constant k. In this paper we shall show that the inclusion L (X) subset of L (Y) implies that Y is more efficient than X. Analogous results are presented for some modifications of the measure of active symbols.
active symbol lindenmayer systems descriptional complexity efficiency of description