On Uniform DOL Words

We introduce the wide class of marked uniform DOL words and study their structure. The criterium of circularity of a marked uniform DOL word is given, and the subword complexity function is found for the uncircular case as well as for the circular one.

[1]  Samuel Eilenberg Automata, Languages and Machines, Vol. B , 1976 .

[2]  B. Mossé Reconnaissabilité des substitutions et complexité des suites automatiques , 1996 .

[3]  Théodore Tapsoba,et al.  Automates calculant la complexité de suites automatiques , 1994 .

[4]  S. V. Avgustinovich The Number of Distinct Subwords of Fixed Length in the Morse-Hedlund Sequence , 1996 .

[5]  Brigitte Mossé,et al.  Puissances de mots et reconnaissabilité des point fixes d'une substitution , 1992, Theor. Comput. Sci..

[6]  Juhani Karhumäki,et al.  Toeplitz Words, Generalized Periodicity and Periodically Iterated Morphisms , 1997, Eur. J. Comb..

[7]  Filippo Mignosi,et al.  If a D0L Language is k-Power Free then it is Circular , 1993, ICALP.

[8]  Aldo de Luca,et al.  Some Combinatorial Properties of the Thue-Morse Sequence and a Problem in Semigroups , 1989, Theor. Comput. Sci..

[9]  Veikko Keränen,et al.  Abelian Squares are Avoidable on 4 Letters , 1992, ICALP.

[10]  Julien Cassaigne An Algorithm to Test if a Given Circular HDOL-Language Avoids a Pattern , 1994, IFIP Congress.

[11]  Brigitte Mosse,et al.  Properties of words and recognizability of fixed points of a substitution , 1992 .

[12]  Anna E. Frid The Subword Complexity of Fixed Points of Binary Uniform Morphisms , 1997, FCT.

[13]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[14]  Srecko Brlek,et al.  Enumeration of factors in the Thue-Morse word , 1989, Discret. Appl. Math..

[15]  Juhani Karhumäki,et al.  Toeplitz Words, Generalized Periodicity and Periodically Iterated Morphisms (Extended Abstract) , 1995, COCOON.