Abstract
Different versions of the notion of almost-periodicity are natural generalizations of the notion of periodicity. The notion of strict almost-periodicity appeared in symbolic dynamics, but later proved to be fruitful in mathematical logic and the theory of algorithms as well. In the paper, a class of essentially almost-periodic sequences (i.e., strictly almost-periodic sequences with an arbitrary prefix added at the beginning) is considered. It is proved that the property of essential almost-periodicity is preserved under finite-automaton transformations, as well as under the action of finite transducers. The class of essentially almost-periodic sequences is contained in the class of almost-periodic sequences. It is proved that this inclusion is strict.
Similar content being viewed by others
Bibliography
M. Morse and G. A. Hedlund, “Symbolic dynamics,” Amer. J. Math., 60 (1938), 815–866.
M. Morse and G. A. Hedlund, “Symbolic dynamics II: Sturmian trajectories,” Amer. J. Math., 62 (1940), 1–42.
An. Muchnik, A. Semenov, and M. Ushakov, “Almost-periodic sequences,” Theoret. Comput. Sci., 304 (2003), 1–33.
A. Weber, “On the valuedness of finite transducers,” Acta Informatica, 27 (1989), 749–780.
Author information
Authors and Affiliations
Additional information
__________
Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 751–756.
Original Russian Text Copyright © 2006 by Yu. L. Pritykin.
Rights and permissions
About this article
Cite this article
Pritykin, Y.L. Finite-automaton transformations of strictly almost-periodic sequences. Math Notes 80, 710–714 (2006). https://doi.org/10.1007/s11006-006-0191-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11006-006-0191-7