ON THE NUMBER OF ACTIVE SYMBOLS IN LINDENMAYER SYSTEMS

Abstract

A symbol a is called active in an L system G if there is a rule a → υ with a ≠ υ in some table of G. By AcX(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 [Formula: see text] and [Formula: see text] satisfy [Formula: see text], we say that Y is more efficient than X, if there is a sequence of languages [Formula: see text], n ≥ 1, such that AcX(Ln) ≥ n and AcY(Ln) ≤ k for some constant k. In this paper we shall show that the inclusion [Formula: see text] implies that Y is more efficient than X. Analogous results are presented for some modifications of the measure of active symbols.