Abstract

An interpretation of a grammar form is called ( k, i)-bounded iff all its nonterminals are substituted by at most k symbols and all its terminals are replaced by at most i words. The ( k, i)-bounded grammar family of a grammar form is the collection of its ( k, i)-bounded interpretations, and its ( k, i)-bounded grammatical family is the corresponding family of languages. The paper gives basic properties of these families. Especially, we show the decidability of the equivalence problem for bounded grammar families, the undecidability of the membership problem for bounded language families and give some hierarchy, closure and descriptional complexity results. Finally, some consequences in normal form theory of context-free languages are presented.

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