Abstract
We prove that if a DOL language is k-power free then it is circular. By using this result we are able to give an algorithm which decides whether, fixed an integer k≥1, a DOL language is k-power free; we are also able to give a new simpler proof of a result, previously obtained by Ehrenfeucht and Rozenberg, that states that it is decidable whether a DOL language is k-power free for some integer k≥1.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
J. Berstel, “Sur les mots sans carré définis par un morphisme”, in Springer Lectures Notes in Computer Science Vol 71 (1979), 16–25.
J. Berstel, “Some recent results on square-free words” (STACS 84) Tech. Rept. L.I.T.P. 84-6.
J. Berstel, “Motifs et répétitions”, in Actes du Congres “Journées Montoises”, 1990, 9–15.
J. Berstel and D. Perrin, “Theory of Codes”, 1985 Academic Press.
F. J. Brandenburg, “Uniformly growing kth power free homomorphisms”, T.C.S. 23 (1983), 69–82.
A. Carpi,“On the size of a square-free morphism on a three letter alphabet”, Inf. Proc. Lett. 16 (1983), 231–235.
A. Cerny,“On a class of infinite words with bounded repetitions”, RAIRO Inf. Th. 19 (1985), 337–349.
C. Choffrut, “Iterated Substitutions and Locally Catenative Systems: a Decidability Result in the Binary Case”, in Proc. ICALP 90,Lecture Notes in Comp. Science, Springer (1990), 490–500.
M. Crochemore, “Sharp Characterizations of square free morphisms” T. C. S. 18 (1982) 221–226.
A. Ehrenfeucht and G. Rozenberg, “On the subword complexity of square-free DOL languages” T.C.S. 16 (1981), 25–32.
A. Ehrenfeucht and G. Rozenberg, “Repetitions in homomorphisms and Languages” in 9th ICALP Symposium, Lecture Notes in Comp. Science, Springer (1982), 192–196.
A. Ehrenfeucht and G. Rozenberg, “Repetitions of Subwords in DOL Languages”, Information and Control 59 (1983), 13–35.
M. Harrison, “Introduction to Formal Language Theory” Addison-Wesley, Readings, Mass., 1978.
Harju and M. Linna,“On the periodicity of morphisms on free monoids”, RAIRO Inf. Th. vol. 20 (1986), nℴ1, 47–54.
B. Host, “Valeurs propres des systèmes dynamiques définis par des substitutions de longueur variable” Erg. Th. and Dyn. Sys. 6 (1986), 529–540.
J. Karhumàki, “On cube free w-words generated by binary morphisms”, in Proc. FCT'81, Lecture Notes in Comp. Science 117, Springer (1981), 182–189.
J. Karhumàki, “On cube free w-words generated by binary morphisms”, Discr. Appl. Math. 5 (1983), 279–297.
V. Keranen, “On the k-freeness of morphisms on free monoids”, STACS 87, Lecture Notes in Comp. Science 247, 180–187.
R. Kfoury, “A linear time algorithm to decide whether a binary word contains an overlap”, RAIRO Inf. Th. 22 (1988), 135–145.
M. Leconte, “kth power free codes” in “Automata on infinite words”, M. Nivat and D. Perrin editors, Lecture Notes in Comp. Science 192, Springer-Verlag, 1984,172–187.
M. Leconte,“A Characterization of power-free morphisms”, T.C.S. 38(1) (1985), 117–122.
A. Lentin and M. P. Schutzenberger, “A combinatorial problem in the theory of free monoids”, in Proc. University of North Carolina, (1967), Boss ed., North Carolina Press, Chapell Hill, 128–144.
Lothaire, “Combinatorics on words”, Addison Wesley, Reading Mass. 1982.
J. C. Martin,“Minimal flows arising from substitutions of non constant length” Math. Sys. Th. 7 (1973), 73–82.
F. Mignosi, “Infinite word with linear subword complexity”, T.C.S. 65 (1989), 221–242.
F. Mignosi, G. Pirillo, “Repetitions in the Fibonacci infinite word”, RAIRO Inf. Th. vol. 26, nℴ 3 (1992), 199–204.
B. Mossé, “Pulssance de mots et reconnaissabilité des points fixes d'une substitution” T.C.S. (1992)
M. Queffeleq,“Substitution dynamical systems — Spectral analysis” Lecture Notes in Math. 1294 (1987), Springer-Verlag.
A. Restivo and S. Salemi, “Overlap free words on two symbols”, in “Automata on infinite words”, M. Nivat and D. Perrin editors, Lecture Notes in Comp.Science 192, Springer-Verlag, 1984,198–206.
P. Séébold, “Sequences generated by infinitely iterated morphisms”, Discr. Appl. Math. 11 (1985), 255–264.
P. Séébold, “An effective solution to the DOL-periodicity problem in the binary case”, EATCS bull. 36 (1988), 137–151.
G. Rozenberg and A. Salomaa, “The mathematical theory of L Systems”, Academic Press, 1980.
G. Rozenberg and A. Salomaa editors, “The book of L”, Springer-Verlag, 1986.
A. Salomaa, “Jewels of Formal Language Theory”, Computer Science Press, Washington, D. C., 1981.
Thue A., “über unendliche Zeichenreihen”, Norske Vid. Selsk. Skr. I. Mat.-Nat. Kl, Christiana 1906, Nr. 7, 1–22.
Thue A., “über die gegenseitige Lege gleicher Teile gewisser Zeichenrein”, Norske Vid. Selsk. Skr. I. Mat.-Nat. Kl., Christiana 1912, Nr. 1, 1–67.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mignosi, F., Séébold, P. (1993). If a DOL language is k-power free then it is circular. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_98
Download citation
DOI: https://doi.org/10.1007/3-540-56939-1_98
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56939-8
Online ISBN: 978-3-540-47826-3
eBook Packages: Springer Book Archive