A MEALY MACHINE WITH POLYNOMIAL GROWTH OF IRRATIONAL DEGREE-Reference-Cited by-同舟云学术

A MEALY MACHINE WITH POLYNOMIAL GROWTH OF IRRATIONAL DEGREE

Published:2008-02 Issue:01 Volume:18 Page:59-82
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

BARTHOLDI LAURENT¹,REZNYKOV ILLYA I.¹

Affiliation:

1. École Polytechnique Fédérale de Lausanne (EPFL), Institut de Mathématiques B (IMB), CH-1015 Lausanne, Switzerland

Abstract

We consider a very simple Mealy machine (two nontrivial 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 ℓα, for [Formula: see text]; that the semigroup satisfies the identity g6 = g4; and that its lattice of two-sided ideals is a chain.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196708004287

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