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On automatic infinite permutations∗

Published online by Cambridge University Press:  23 November 2011

Anna Frid  and
Luca Zamboni
Anna Frid
Affiliation:
Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090 Novosibirsk, Russia.. [email protected] Institut Camille Jordan, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France.; [email protected].
Luca Zamboni
Affiliation:
Institut Camille Jordan, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France.; [email protected]. Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland.
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Abstract

An infinite permutation α is a linear ordering of N. We study properties of infinite permutations analogous to those of infinite words, and show some resemblances and some differences between permutations and words. In this paper, we try to extend to permutations the notion of automaticity. As we shall show, the standard definitions which are equivalent in the case of words are not equivalent in the context of permutations. We investigate the relationships between these definitions and prove that they constitute a chain of inclusions. We also construct and study an automaton generating the Thue-Morse permutation.

Keywords

Permutationinfinite permutationorderinginfinite wordautomatic wordautomatic permutationThue-Morse wordThue-Morse permutation
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 1: Special issue dedicated to the 13th "Journées Montoises d'Informatique Théorique" , January 2012 , pp. 77 - 85
Copyright
© EDP Sciences 2011

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