On the number of nonterminals in linear conjunctive grammars

AbstractThe number of nonterminals in a linear conjunctive grammar is considered as a descriptional complexity measure of this family of languages. It is proved that a hierarchy collapses, and for every linear conjunctive grammar there exists and can be effectively constructed a linear conjunctive grammar that accepts the same language and contains exactly two nonterminals. This yields a partition of linear conjunctive languages into two nonempty disjoint classes of those with nonterminal complexity 1 and 2. The basic properties of the family of languages for which one nonterminal suffices are established. Nonterminal complexity of grammars in the linear normal form is also investigated