Year: 2008
Type: article
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.
Authors: LAURENT BARTHOLDI, ILLYA I. REZNYKOV
Institution: École Polytechnique Fédérale de Lausanne
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2073963798