On the nonterminal complexity of tree controlled grammars

Abstract

A tree controlled grammar is a regulated rewriting device which can be given as a pair (G,R) where G is a context-free grammar and R is a regular set over the terminal and nonterminal alphabets of G. The language generated by the tree controlled grammar contains those words of L(G) which have a derivation tree where all the words obtained by reading the symbols labeling the nodes belonging to the different levels of the tree, from left to right, belong to the language R. The nonterminal complexity of tree controlled grammars can be given as the number of nonterminals of the context-free grammar G, and the number of nonterminals that a regular grammar needs to generate the control language R. Here we improve the currently known best upper bound on the nonterminal complexity of tree controlled grammars from seven to six, that is, we show that a context-free grammar with five nonterminals and a control language which can be generated by a grammar with one nonterminal is sufficient to generate any recursively enumerable language. © 2012 Springer-Verlag Berlin Heidelberg.