Periodic and Sturmian languages

Authors:
Lucian Ilie;Solomon Marcus;Ion Petre
Affiliations:
Department of Computer Science, University of Western Ontario, London, ON, Canada;Romanian Academy, Mathematics, Calea Victoriei, Bucharest, Romania;Department of Computer Science, Åbo Akademi University, Turku, Finland
Venue:
Information Processing Letters
Year:
2006

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Abstract

Counting the number of distinct factors in the words of a language gives a measure of complexity for that language similar to the factor-complexity of infinite words. Similarly as for infinite words, we prove that this complexity function f(n) is either bounded or f(n) ≥ n + 1. We call languages with bounded complexity periodic and languages with complexity f(n) = n + 1 Sturmian. We describe the structure of periodic languages and characterize the Sturmian languages as the sets of factors of (one-or two-way) infinite Sturmian words.