Geodesic
Periodic functions on a free semigroup
Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1509-1528 
V. L. Kurakin. Periodic functions on a free semigroup. Sbornik. Mathematics, Tome 197 (2006) no. 10, pp. 1509-1528. http://geodesic.mathdoc.fr/item/SM_2006_197_10_a6/
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     author = {V. L. Kurakin},
     title = {Periodic functions on a free semigroup},
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     year = {2006},
     volume = {197},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_10_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $X^*$ be the set of words over a finite alphabet $X$. The concept of periodic function $u\colon X^*\to M$ is considered. Such functions arise as the state transition functions and the output functions of automata. A method for the evaluation of the period and other characteristics of a periodic function with the use of the vector-period group and the fundamental group of the graph of the function is put forward. Bibliography: 5 titles.

[1] V. B. Kudryavtsev , S. V. Aleshin, A. S. Podkolzin, Vvedenie v teoriyu avtomatov, Nauka, M., 1985 | MR | Zbl

[2] V. L. Kurakin, “Svobodnye registry sdviga. I”, Trudy po diskretnoi matematike, 9, Gelios ARV, M., 2006, 77–109

[3] V. L. Kurakin, A. S. Kuzmin, A. V. Mikhalev, A. A. Nechaev, “Linear recurring sequences over rings and modules”, J. Math. Sci. (New York), 76:6 (1995), 2793–2915 | DOI | MR | Zbl

[4] M. Kholl, Teoriya grupp, IL, M., 1962 | MR | Zbl

[5] O. V. Bogopolskii, Vvedenie v teoriyu grupp, Institut kompyuternykh issledovanii, M., Izhevsk, 2002