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.
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