Families Generated by Grammars and L Systems

Abstract

Grammars appear in many chapters of this Handbook, often constituting the key notion of the chapter. Usually a specific language, L(G), is associated to a grammar G. The language L(G) is generated by the grammar G,obtained from a specific starting point by rules specified in the grammar. In this chapter we take a more general point of view. A grammar G defines a collection of structurally similar grammars G’, called interpretations of G. Each of the interpretations G’,in turn, generates a language L(G’) in the usual way. In this chapter we consider the family\( \mathcal{L} \)(G) of languages L(G’) generated by the interpretations G’ of G. The family \( \mathcal{L} \)(G) is referred to as the grammatical family associated to G. Thus, from the point of view taken in this chapter, grammars generate families of languages rather than single languages. When grammars are considered in this way, the term “grammar form” rather than “grammar” will be used. As constructs grammar forms and grammars are identical. However, they are applied in different ways. We will consider also L forms, that is L systems applied similarly, defining language families via interpretations.