Abstract
We give in the following a definition of the complexity function of an infinite sequence on a finite alphabet. This function measures in some sense the predictability of the sequence. It is defined as the counting function of blocks of length n occurring in the given sequence. These blocks can be arranged in graphs and we study in a peculiar case (sturmian sequences) the evolution of these graphs. It turns out that low complexity implies strong geometrical properties of the sequence viewed as the itinerary of a point in some dynamical system. This field of research is rich of yet unsolved problems.
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© 1996 Springer Science+Business Media Dordrecht
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Rauzy, G. (1996). Low Complexity and Geometry. In: Goles, E., MartÃnez, S. (eds) Dynamics of Complex Interacting Systems. Nonlinear Phenomena and Complex Systems, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1323-8_4
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DOI: https://doi.org/10.1007/978-94-017-1323-8_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4734-2
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