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.
@article{ITA_2001__35_6_525_0, author = {Carton, Olivier and Choffrut, Christian}, title = {Periodicity and roots of transfinite strings}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {525--533}, publisher = {EDP-Sciences}, volume = {35}, number = {6}, year = {2001}, mrnumber = {1922293}, zbl = {1005.68120}, language = {en}, url = {http://archive.numdam.org/item/ITA_2001__35_6_525_0/} }
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 SP - 525 EP - 533 VL - 35 IS - 6 PB - EDP-Sciences UR - http://archive.numdam.org/item/ITA_2001__35_6_525_0/ LA - en ID - ITA_2001__35_6_525_0 ER -
%0 Journal Article %A Carton, Olivier %A Choffrut, Christian %T Periodicity and roots of transfinite strings %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2001 %P 525-533 %V 35 %N 6 %I EDP-Sciences %U http://archive.numdam.org/item/ITA_2001__35_6_525_0/ %G en %F ITA_2001__35_6_525_0
Carton, Olivier; Choffrut, Christian. Periodicity and roots of transfinite strings. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 6, pp. 525-533. http://archive.numdam.org/item/ITA_2001__35_6_525_0/
[1] Periodic-like words, periodicity and boxes. Acta Informatica 37 (2001) 597-618. | MR | Zbl
and ,[2] Une caractérisation des mots périodiques. C. R. Acad. Sci. Paris A (1978) 1175-1177. | MR | Zbl
and ,[3] Transfinite equations in transfinite strings, 625-649. | MR | Zbl
and ,[4] Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci. 9 (1979) 17-26. | MR | Zbl
,[5] Mots de Lyndon et périodicité. RAIRO: Theoret. Informatics Appl. 14 (1980) 181-191. | Numdam | MR | Zbl
,[6] Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 3 (1965) 109-114. | MR | Zbl
and ,[7] A periodicity theorem fro trees. Theoret. Comput. Sci. 1-2 (1998) 145-181. | MR | Zbl
, , and ,[8] Allgemeine Mengenlehre. Akademie Verlag (1969). | MR | Zbl
,[9] Linear ordering. Academic Press, New York (1982). | MR | Zbl
,[10] Cardinal and Ordinal Numbers. Warsaw: PWN (1958). | MR | Zbl
,