Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
Hostname: page-component-7ccbd9845f-2c279 Total loading time: 0.238 Render date: 2023-02-01T18:59:57.194Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true
  • English
RAIRO - Theoretical Informatics and Applications RAIRO - Theoretical Informatics and Applications

Article contents

Periodicity and roots of transfinite strings

Published online by Cambridge University Press:  15 July 2002

Olivier Carton  and
Christian Choffrut
Olivier Carton
Affiliation:
Institut Gaspard Monge, CNRS, Université de Marne-la-Vallée 5, boulevard Descartes, 77454 Marne-la-Vallée Cedex 2, France; (Olivier.Carton@univ-mlv.fr)
Christian Choffrut
Affiliation:
LIAFA, Université Paris 7, étage, bureau 6A7, 175 rue du Chevaleret, 75013 Paris, France; (Christian.Choffrut@liafa.jussieu.fr)
Get access

Abstract

This contribution extends the notions of roots and periodicity to strings of transfinite lengths. It shows that given a transfinite string, either it possesses a unique root or the set of its roots are equivalent in a strong way.

Keywords

Ordinalscombinatorics on words.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 6: A tribute to Aldo de Luca , November 2001 , pp. 525 - 533
Copyright
© EDP Sciences, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Carpi, A. and de Luca, A., Periodic-like words, periodicity and boxes. Acta Informatica 37 (2001) 597-618. CrossRef
Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C. R. Acad. Sci. Paris A (1978) 1175-1177.
C. Choffrut and S. Horváth, Transfinite equations in transfinite strings, 625-649.
Duval, J.P., Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci. 9 (1979) 17-26. CrossRef
Duval, J.P., Mots de Lyndon et périodicité. RAIRO: Theoret. Informatics Appl. 14 (1980) 181-191.
Fine, N.J. and Wilf, H.S., Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 3 (1965) 109-114. CrossRef
Giammarresi, D., Mantaci, S., Mignosi, F. and Restivo, A., A periodicity theorem fro trees. Theoret. Comput. Sci. 1-2 (1998) 145-181. CrossRef
D. Klaua, Allgemeine Mengenlehre. Akademie Verlag (1969).
J.G. Rosenstein, Linear ordering. Academic Press, New York (1982).
W. Sierpinski, Cardinal and Ordinal Numbers. Warsaw: PWN (1958).

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Periodicity and roots of transfinite strings
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Periodicity and roots of transfinite strings
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Periodicity and roots of transfinite strings
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *