A MEALY MACHINE WITH POLYNOMIAL GROWTH OF IRRATIONAL DEGREE
Laurent Bartholdi, Illya, I. Reznykov · 2007
Abstract. We consider a very simple Mealy machine (two non-trivial states over a two-symbol alphabet), and derive some properties of the semigroup it generates. It is an infinite, finitely generated semigroup, and we show that the growth function of its balls behaves asymptotically like nα, for α = 1 + log 2/log 1+√5; that the semigroup satisfies the identity g 2 6 = g4; and that its lattice of two-sided ideals is a chain. 1.