Drunken man infinite words complexity

Issue		RAIRO-Theor. Inf. Appl. Volume 42, Number 3, July-September 2008 JM'06


Page(s)		599 - 613
DOI		10.1051/ita:2008012
Published online		03 June 2008

RAIRO-Theor. Inf. Appl. 42, 599-613 (2008)
DOI: 10.1051/ita:2008012

Marion Le Gonidec

Institut de Mathématiques, Université de Liège, Grande traverse 12 B.37, 4000 Liège, Belgium; M.LeGonidec@ulg.ac.be

Published online: 3 June 2008

Abstract
In this article, we study the complexity of drunken man infinite words. We show that these infinite words, generated by a deterministic and complete countable automaton, or equivalently generated by a substitution over a countable alphabet of constant length, have complexity functions equivalent to $n(\log_2 n)^2$ when n goes to infinity.

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