Substitution expressions

摘要

This paper describes a characterization of context-free languages by means of expressions using union, substitution, and an iterative substitution called substitution star. The “substitution expressions” so defined have some properties analogous to those of regular expressions. The well-known cases of linear and regular subfamilies of context-free languages are obtainable from the general model by placing proper restrictions on the basis over which the substitution expressions are defined. The notion of substitution star height of a substitution expression is defined analogously to regular star height for regular expressions. It shown that for each n≥0 there exists a context-free, in fact, linear language whose substitution star height is n.