Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-23T07:51:43.306Z Has data issue: false hasContentIssue false
  • English
  • Français

A test-set for k-power-free binary morphisms

Published online by Cambridge University Press:  15 August 2002

F. Wlazinski
F. Wlazinski*
Affiliation:
LaRIA, Université de Picardie Jules Verne, 5 rue du Moulin Neuf, 80000 Amiens, France; [email protected].
Get access

Abstract

A morphism f is k-power-free if and only if f(w) is k-power-free whenever w is a k-power-free word.A morphism f is k-power-free up to m if and onlyif f(w) isk-power-free whenever w is a k-power-free word of length at most m.Given an integer k ≥ 2,we prove that a binary morphism is k-power-freeif and only if it is k-power-free up to k 2.This bound becomes linear for primitive morphisms:a binary primitive morphism is k-power-freeif and only if it is k-power-free up to 2k+1

Keywords

Combinatorics on wordsk-power-free wordsmorphismstest-sets
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 5 , September 2001 , pp. 437 - 452
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

J. Berstel, Axel thue's work on repetitions in words, edited by P. Leroux and C. Reutenauer, Séries formelles et combinatoire algébrique. LaCIM, University of Québec at Montréal (1992) 65-80.
J. Berstel, Axel thue's papers on repetitions in words: A translation, Technical Report 20. LaCIM, University of Québec at Montréal (1995).
Berstel, J. and Séébold, P., A characterization of overlap-free morphisms. Discrete Appl. Math. 46 (1993) 275-281. CrossRef
Crochemore, M., Sharp characterizations of squarefree morphisms. Theoret. Comput. Sci. 18 (1982) 221-226. CrossRef
Karhumäki, J., On cube free ω-words generated by binary morphisms. Discrete Appl. Math. 5 (1983) 279-297. CrossRef
Keränen, V., On the k-repetition freeness of length uniform morphisms over a binary alphabet. Discrete Appl. Math. 9 (1984) 297-300. CrossRef
V. Keränen, On the k-freeness of morphisms on free monoids. Ann. Acad. Sci. Fenn. 61 (1986).
Leconte, M., A characterization of power-free morphisms. Theoret. Comput. Sci. 38 (1985) 117-122. CrossRef
M. Leconte, Codes sans répétition, Ph.D. Thesis. LITP Université P. et M. Curie (1985).
A. Lentin and M.P. Schützenberger, A combinatorial problem in the theory of free monoids, edited by R.C. Bose and T.E. Dowling. Chapell Hill, North Carolina Press edition, Comb. Math. (1945) 112-144.
M. Lothaire, Combinatorics on words, Vol. 17 of Encyclopedia of Mathematics, Chap. 9, Equations on words. Addison-Wesley (1983). Reprinted in 1997 by Cambridge University Press in the Cambridge Mathematical Library.
M. Lothaire, Algebraic combinatorics on words. Cambridge University Press (to appear).
Mitrana, V., Primitive morphisms. Inform. Process. Lett. 64 (1997) 277-281. CrossRef
Morse, M., Recurrent geodesics on a surface of negative curvature. Trans. Amer. Math. Soc. 22 (1921) 84-100. CrossRef
Richomme, G. and Séébold, P., Characterization of test-sets for overlap-free morphisms. Discrete Appl. Math. 98 (1999) 151-157. CrossRef
G. Richomme and F. Wlazinski, About cube-free morphisms, edited by H. Reichel and S. Tison, STACS 2000. Springer-Verlag, Lecture Notes in Comput. Sci. 1770 (2000) 99-109.
Richomme, G. and Wlazinski, F., Some results on k-power-free morphisms. Theoret. Comput. Sci. 273 (2002) 119-142. CrossRef
Séébold, P., Sequences generated by infinitely iterated morphisms. Discrete Appl. Math. 11 (1985) 255-264. CrossRef
A. Thue, Uber unendliche Zeichenreihen. Videnskapsselskapets Skrifter, I. Mat.-naturv. Klasse, Kristiania (1906) 1-22.
A. Thue, Uber die gegenseitige Lage gleigher Teile gewisser Zeichenreihen. Videnskapsselskapets Skrifter, I. Mat.-naturv. Klasse, Kristiania (1912) 1-67.