Periodicity and roots of transfinite strings

Olivier Carton; Christian Choffrut

RAIRO - Theoretical Informatics and Applications (2010)

  • 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 35.6 (2010): 525-533. <http://eudml.org/doc/222003>.

@article{Carton2010,
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},
keywords = {Ordinals; combinatorics on words.; roots; strings of transfinite lengths},
language = {eng},
month = {3},
number = {6},
pages = {525-533},
publisher = {EDP Sciences},
title = {Periodicity and roots of transfinite strings},
url = {http://eudml.org/doc/222003},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Carton, Olivier
AU - Choffrut, Christian
TI - Periodicity and roots of transfinite strings
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
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/222003
ER -

References

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  1. A. Carpi and A. de Luca, Periodic-like words, periodicity and boxes. Acta Informatica37 (2001) 597-618.  Zbl0973.68192
  2. Y. Césari and M. Vincent, Une caractérisation des mots périodiques. C. R. Acad. Sci. Paris A (1978) 1175-1177.  Zbl0392.20039
  3. C. Choffrut and S. Horváth, Transfinite equations in transfinite strings, 625-649.  Zbl1007.68140
  4. J.P. Duval, Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci.9 (1979) 17-26.  Zbl0402.68052
  5. J.P. Duval, Mots de Lyndon et périodicité. RAIRO: Theoret. Informatics Appl.14 (1980) 181-191.  Zbl0444.20048
  6. N.J. Fine and H.S. Wilf, Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc.3 (1965) 109-114.  Zbl0131.30203
  7. D. Giammarresi, S. Mantaci, F. Mignosi and A. Restivo, A periodicity theorem fro trees. Theoret. Comput. Sci.1-2 (1998) 145-181.  Zbl0913.68150
  8. D. Klaua, Allgemeine Mengenlehre. Akademie Verlag (1969).  
  9. J.G. Rosenstein, Linear ordering. Academic Press, New York (1982).  Zbl0488.04002
  10. W. Sierpinski, Cardinal and Ordinal Numbers. Warsaw: PWN (1958).  Zbl0083.26803

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