An Algorithm for Recognizing the Spherical Transitivity of an Initial Binary Automaton

T. I. Lipina

Lomonosov Moscow State University

Abstract: 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.

UDC: 519.713

Received: 20.05.2020
Revised: 18.06.2020

DOI: 10.4213/mzm12540

 English version: Mathematical Notes, 2020, 108:5, 721–726

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