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On the subword complexity of DOL languages with a constant distribution. (English) Zbl 0546.68062

For a language \(L\subseteq\Sigma^*\), let sub(L) [resp. \(sub_ n(L)]\) denote the set of all subwords [resp. the set of all subwords of length n] occurring in the words of L. For each n, let \(\pi_ L(n)\) be the cardinality of \(sub_ n(L)\). The authors say that a language \(L\subseteq\Sigma^*\) has a constant distribution if there exist a positive integer C and an alphabet \(\Delta \subseteq\Sigma \) such that every word \(\alpha \in sub(L)\) with \(|\alpha |\geq C\) satisfies \(alph(\alpha)=\Delta.\) The paper contains the following results. If L is a DOL language that has a constant distribution, then there exists a positive integer Q such that \(\pi_ L(n)\leq Qn\) for every positive integer n. Moreover, there exists a DOL language L that has a constant distribution and is such that \(\pi_ L(n)\geq n\) for every positive integer n.

MSC:

68Q45 Formal languages and automata
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[1] Berstel, J., Sur LES mots sans carré définis par un morphisme, (), 16-25 · Zbl 0425.20046
[2] A. Ehrenfeucht and G. Rozenberg. On subword complexities of homomorphic images of languages, Rev. Fr. Automat. Inform. Rech. Opér., Sér. Rouge, to appear. · Zbl 0495.68069
[3] A. Ehrenfeucht and G. Rozenberg, On the subword complexity of square-free DOL languages, Theoret. Comput. Sci., to appear. · Zbl 0481.68073
[4] Rozenberg, G.; Salomaa, A., The mathematical theory of L systems, (1980), Academic Press London · Zbl 0365.68072
[5] Salomaa, A., Morphisms on free monoids and language theory, ()
[6] A. Salomaa, Jewels of Language Theory, Computer Science Press, to appear. · Zbl 0487.68063
[7] Thue, A., Über unendliche zeichenreihen, Norske vid. selsk. skr. I math.-nat. KI., 7, 1-22, (1906) · JFM 39.0283.01
[8] Thue, A., Über die gegenseitige lage gleicher teile gewisser zeichenreihen, Norske vid. skr. I math.-nat., 1, 1-67, (1912) · JFM 44.0462.01
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