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A Mealy machine with polynomial growth of irrational degree

Laurent Bartholdi·Illya I. Reznykov
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Abstract

We consider a very simple Mealy machine (three states over a two-symbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, finitely generated semigroup; we show that the growth function of its balls behaves asymptotically like n^2.4401..., where this constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfies the identity g^6=g^4; and that its lattice of two-sided ideals is a chain.

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Laurent Bartholdi, Illya I. Reznykov. 2007-01-12. A Mealy machine with polynomial growth of irrational degree. https://doi.org/10.1142/s0218196708004287

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