Nonterminal complexity of programmed grammars

We show that, in the case of context-free programmed grammars with appearance checking working under free derivations, three nonterminals are enough to generate every recursively enumerable language. This improves the previously published bound of eight for the nonterminal complexity of these grammars. This also yields an improved nonterminal complexity bound of four for context-free matrix grammars with appearance checking. Moreover, we establish nonterminal complexity bounds for context-free programmed and matrix grammars working under leftmost derivations.

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