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research article
A mealy machine with polynomial growth of irrational degree
Bartholdi, Laurent
•
Reznykov, Illya I.
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 l(alpha), for alpha = 1 + log 2/log 1+root 5/2 ; that the semigroup satisfies the identity g(6) = g(4); and that its lattice of two-sided ideals is a chain.
Type
research article
Web of Science ID
WOS:000254194500003
Authors
Bartholdi, Laurent
•
Reznykov, Illya I.
Publication date
2008
Published in
Volume
18
Start page
59
End page
82
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
November 30, 2010
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