Language classes generated by tree controlled grammars with bounded nonterminal complexity

Abstract

A tree controlled grammar can be given as a pair (G,G′) where G is a context-free grammar and G′ is a regular grammar. Its language consists of all terminal words with a derivation in G such that all levels of the corresponding derivation tree - except the last level - belong to L(G′). We define its descriptional complexity Var(G,G′) as the sum of the numbers of nonterminals of G and G′. In [24] we have shown that tree controlled grammars (G,G′) with Var(G,G′)∈≥∈9 are sufficient to generate all recursively enumerable languages. In this paper, our main result improves the bound to seven. Moreover, we show that all linear and regular simple matrix languages can be generated by tree controlled grammars with a descriptional complexity bounded by three. © 2011 Springer-Verlag Berlin Heidelberg.