## 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

### Keywords:

subword complexity; DOL language; constant distribution
Full Text:

### References:

 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.