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

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.