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}, volume = {35}, year = {2001}, pages = {525-533}, mrnumber = {1922293}, zbl = {1005.68120}, language = {en}, url = {http://dml.mathdoc.fr/item/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, Tome 35 (2001) pp. 525-533. http://gdmltest.u-ga.fr/item/ITA_2001__35_6_525_0/
[1] Periodic-like words, periodicity and boxes. Acta Informatica 37 (2001) 597-618. | MR 1830469 | Zbl 0973.68192
and ,[2] Une caractérisation des mots périodiques. C. R. Acad. Sci. Paris A (1978) 1175-1177. | MR 501107 | Zbl 0392.20039
and ,[3] Transfinite equations in transfinite strings, 625-649. | MR 1781851 | Zbl 1007.68140
and ,[4] Périodes et répétitions des mots du monoïde libre. Theoret. Comput. Sci. 9 (1979) 17-26. | MR 535121 | Zbl 0402.68052
,[5] Mots de Lyndon et périodicité. RAIRO: Theoret. Informatics Appl. 14 (1980) 181-191. | Numdam | MR 581676 | Zbl 0444.20048
,[6] Uniqueness theorems for periodic functions. Proc. Amer. Math. Soc. 3 (1965) 109-114. | MR 174934 | Zbl 0131.30203
and ,[7] A periodicity theorem fro trees. Theoret. Comput. Sci. 1-2 (1998) 145-181. | MR 1638652 | Zbl 0913.68150
, , and ,[8] Allgemeine Mengenlehre. Akademie Verlag (1969). | MR 242680 | Zbl 0165.31204
,[9] Linear ordering. Academic Press, New York (1982). | MR 662564 | Zbl 0488.04002
,[10] Cardinal and Ordinal Numbers. Warsaw: PWN (1958). | MR 95787 | Zbl 0083.26803
,