On lengths of words in context-free languages

We consider slender languages, that is, languages for which the number of words of the same length is bounded from above by a constant. We prove that the slenderness problem is decidable for context-free languages and that the maximal number of words of the same length in a given context-free language is computable. Some effective representations of slender context-free languages, as well as other related decidability problems are investigated.

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