Periodicity and roots of transfinite strings

Olivier Carton; Christian Choffrut

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

  • Volume: 35, Issue: 6, page 525-533
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Carton, Olivier, and Choffrut, Christian. "Periodicity and roots of transfinite strings." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.6 (2001): 525-533. <http://eudml.org/doc/92682>.

@article{Carton2001,
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.},
author = {Carton, Olivier, Choffrut, Christian},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {ordinals; combinatorics on words; roots; strings of transfinite lengths},
language = {eng},
number = {6},
pages = {525-533},
publisher = {EDP-Sciences},
title = {Periodicity and roots of transfinite strings},
url = {http://eudml.org/doc/92682},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Carton, Olivier
AU - Choffrut, Christian
TI - Periodicity and roots of transfinite strings
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 6
SP - 525
EP - 533
AB - 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.
LA - eng
KW - ordinals; combinatorics on words; roots; strings of transfinite lengths
UR - http://eudml.org/doc/92682
ER -

References

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  1. [1] A. Carpi and A. de Luca, Periodic-like words, periodicity and boxes. Acta Informatica 37 (2001) 597-618. Zbl0973.68192MR1830469
  2. [2] Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C. R. Acad. Sci. Paris A (1978) 1175-1177. Zbl0392.20039MR501107
  3. [3] C. Choffrut and S. Horváth, Transfinite equations in transfinite strings, 625-649. Zbl1007.68140MR1781851
  4. [4] J.P. Duval, Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci. 9 (1979) 17-26. Zbl0402.68052MR535121
  5. [5] J.P. Duval, Mots de Lyndon et périodicité. RAIRO: Theoret. Informatics Appl. 14 (1980) 181-191. Zbl0444.20048MR581676
  6. [6] N.J. Fine and H.S. Wilf, Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 3 (1965) 109-114. Zbl0131.30203MR174934
  7. [7] D. Giammarresi, S. Mantaci, F. Mignosi and A. Restivo, A periodicity theorem fro trees. Theoret. Comput. Sci. 1-2 (1998) 145-181. Zbl0913.68150MR1638652
  8. [8] D. Klaua, Allgemeine Mengenlehre. Akademie Verlag (1969). Zbl0165.31204MR242680
  9. [9] J.G. Rosenstein, Linear ordering. Academic Press, New York (1982). Zbl0488.04002MR662564
  10. [10] W. Sierpiński, Cardinal and Ordinal Numbers. Warsaw: PWN (1958). Zbl0083.26803MR95787

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