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Decision Problems Concerning Thinness and Slenderness of Formal Languages
 ACTA INFORM
, 1998
"... A language L is called thin if for almost all n there is at most one word of length n in L. A language L is called slender if there is a positive integer k such that for any n there are at most k words of length n in L. The notions of Parikh thin and Parikh slender languages are defined similarly by ..."
Abstract

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A language L is called thin if for almost all n there is at most one word of length n in L. A language L is called slender if there is a positive integer k such that for any n there are at most k words of length n in L. The notions of Parikh thin and Parikh slender languages are defined similarly by counting the words with the same Parikh vectors instead of the words of the same length. In this paper we discuss decision problems concerning these four properties. It is shown that all four properties are decidable for bounded semilinear languages but undecidable for DT0L languages. As a consequence all problems are decidable for contextfree languages.