Abstract
We obtain a formula for the subword complexity of every binary DOL word which is a fixed point of a uniform morphism, i.e. a morphism in which the images of all letters have the same length. We establish that the complexity function can be found from its values for little lengths and some simple parameters of the morphism. The property of circularity is important for the view of the formula. In general case the subword complexity function has much the same behavour as the complexity function of the Thue-Morse word.
The proof of the formula is based on the properties of the function of first differences of subword complexity and some relations among subword complexity values.
Supported in part by the Russian Foundation for Fundamental Research (Grant 96-01-01800)
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References
Avgustinovich, S. V.: The number of distinct subwords of fixed length in the Morse-Hedlund sequence. Sibirsk. zhurnal issledovaniya operatsii. 1 no. 2 (1994) 3–7
Brlek, S.: Enumeration of factors in the Thue Morse word. Discr. Appl. Math. 24 (1989) 83–96
Cassaigne, J.: An algorithm to test if a given circular HDOL-language avoids a pattern. IFIP World Computer Congress'94. Elsevier (North-Holland) 1 (1994) 459–464
Cassaigne, J.: Special factors of sequences with linear subword complexity. Developments in Language Theory. World Scientific (1996) 25–34
Frid, A.: On the subword complexity of symbolic sequences generated by morphisms. Diskretnyi analiz i issledovaniye operatsii 4 no. 1 (1997) 53–59 (in Russian)
Frid, A.: On the uncircular uniform DOL words. In preparation.
de Luca, A., Varrichio, S.: Some combinatorial properties of the Thue-Morse sequence and a problem of semi groups. Theoret. Comp. Sci. 63 (1989) 333–348
Mignosi, F., Séébold, P.: If a DOL language is k-power-free then it is circular. ICALP'93, Lect. Notes Comp. Sci., no. 700 (1993)
Mossé, B.: Puissances de mots et reconnaissabilité des points fixes d'une substitution. Theoret. Comp. Sci. 99 (1992) 327–334
Mossé, B.: Reconnaissabilité des substitutions et complexité des suites automatiques. Bulletin de la Société Mathématique de France 124 (1996) 329–346
Tapsoba, T.: Automates calculant la complexité des suites automatiques. Journal de Théorie des Nombres de Bordeaux 6 (1994) 127–134 *** DIRECT SUPPORT *** A0008123 00006
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© 1997 Springer-Verlag Berlin Heidelberg
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Frid, A.E. (1997). The subword complexity of fixed points of binary uniform morphisms. In: Chlebus, B.S., Czaja, L. (eds) Fundamentals of Computation Theory. FCT 1997. Lecture Notes in Computer Science, vol 1279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036182
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DOI: https://doi.org/10.1007/BFb0036182
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