Geodesic
An Algorithm for Recognizing the Spherical Transitivity of an Initial Binary Automaton
Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 757-763.

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An algorithm is presented which determines in a finite number of steps whether an initial finite binary automaton is spherically transitive. Since the class of deterministic functions coincides with the class of functions satisfying the Lipschitz condition with constant 1 on the ring of $p$-adic integers, the algorithm is based on an ergodicity criterion for a deterministic function given by a van der Put series.
Keywords: spherical transitivity, initial automaton, $p$-adic number, van der Put series. 
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T. I. Lipina. An Algorithm for Recognizing the Spherical Transitivity of an Initial Binary Automaton. Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 757-763. http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a9/

[1] L. Bartholdi, R. I. Grigorchuk, Z. Šuniḱ, “Branch groups”, Handb. Algebr., 3, North-Holland, Amsterdam, 2003, 989–1112 | MR

[2] R. I. Grigorchuk, V. V. Nekrashevich, V. I. Suschanskii, “Avtomaty, dinamicheskie sistemy i gruppy”, Dinamicheskie sistemy, avtomaty i beskonechnye gruppy, Tr. MIAN, 231, Nauka, MAIK «Nauka/Interperiodika», M., 2000, 134–214 | MR | Zbl

[3] A. G. Lunts, “$p$-adicheskii apparat teorii konechnykh avtomatov”, Probl. kibernet., 14 (1965), 17–30 | Zbl

[4] V. Anashin, “The non-Archimedean theory of discrete systems”, Math. Comput. Sci., 6:4 (2012), 375–393 | MR | Zbl

[5] V. Anashin, A. Khrennikov, E. Yurova, “T-functions revisited: new criteria for bijectivity/transitivity”, Des. Codes Cryptogr., 71:3 (2014), 383–407 | MR | Zbl

[6] V. Anashin, “Automata finiteness criterion in terms of van der Put series of automata functions”, p-Adic Numbers Ultrametric Anal. Appl., 4:2 (2012), 151–160 | MR | Zbl

[7] K. Mahler, $p$-Adic Numbers and Their Functions, Cambridge Univ. Press, Cambridge, 1981 | MR | Zbl

[8] V. Anashin, A. Khrennikov, Applied Algebraic Dynamics, Walter de Gruyter, Berlin, 2009 | MR | Zbl

[9] V. S. Anashin, A. Yu. Khrennikov, E. I. Yurova, “Kharakterizatsiya ergodicheskikh $p$-adicheskikh dinamicheskikh sistem v terminakh bazisa van der Puta”, Dokl. An, 438:2 (2011), 151–153 | MR | Zbl