On Parikh Slender Languages and Power Series

摘要

We define and study Parikh slender languages and power series. A language is Parikh slender if the number of words in the language with the same Parikh vector is bounded from above. As an application we get a new method for ambiguity proofs of context-free languages and a new proof of an earlier result of Autebert, Flajolet, and Gabarro concerning prefixes of infinite words.