Comparing complexity functions of a language and its extendable part. (English) Zbl 1149.68055

Summary: The right (left, two-sided) extendable part of a language consists of all words having infinitely many right (resp. left, two-sided) extensions within the language. We prove that for an arbitrary factorial language each of these parts has the same growth rate of complexity as the language itself. On the other hand, we exhibit a factorial language which grows superpolynomially, while its two-sided extendable part grows only linearly.


68Q45 Formal languages and automata
68R15 Combinatorics on words
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