Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T17:41:28.082Z Has data issue: false hasContentIssue false
  • English
  • Français

On Conjugacy of Languages

Published online by Cambridge University Press:  15 July 2002

Julien Cassaigne ,
Juhani Karhumäki  and
Ján Maňuch
Julien Cassaigne
Affiliation:
Institut de Mathématiques de Luminy – CNRS/FRUMAM, Case 907, 13288 Marseille Cedex 9, France; (cassaigne@iml.univ-mrs.fr)
Juhani Karhumäki
Affiliation:
Department of Mathematics and TUCS, University of Turku, 20014 Turku, Finland; (karhumak@cs.utu.fi)
Ján Maňuch
Affiliation:
TUCS and Department of Mathematics, Datacity, Lemminkäisenkatu 14A, 20520 Turku, Finland; (manuch@cs.utu.fi)
Get access

Abstract

We say that two languages X and Y are conjugates if they satisfy the conjugacy equationXZ = ZY for some language Z. We study several problems associated with this equation. For example, we characterize all sets which are conjugated via a two-element biprefix set Z, as well as all two-element sets which are conjugates.

Keywords

Conjugacy equationlanguagesConway's Problem.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 6: A tribute to Aldo de Luca , November 2001 , pp. 535 - 550
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

Ch. Choffrut and J. Karhumäki, Combinatorics of words, in Handbook of Formal Languages, Vol. 1, edited by G. Rozenberg and A. Salomaa. Springer (1997) 329-438.
Ch. Choffrut, J. Karhumäki, N. Ollinger, The commutation of finite sets: A challenging problem. Theoret. Comput. Sci. 273 (2002) 69-79. CrossRef
J.H. Conway, Regular algebra and finite machines. Chapman Hall (1971).
S. Eilenberg, Automata, languages and machines. Academic Press (1974).
T. Harju, J. Karhumäki and W. Plandowski, Independent systems of equations, Chap. 14 of Algebraic combinatorics on words, by M. Lothaire. Cambridge University Press (2002).
T. Harju and I. Petre, On commutation and primitive roots of codes. TUCS Technical Report 402 (2001).
Karhumäki, J., Combinatorial and computational problems of finite sets of words, in Proc. of MCU'01. Springer, Lecture Notes in Comput. Sci. 2055 (2001) 69-81. CrossRef
Karhumäki, J. and Petre, I., On the centralizer of a finite set, in Proc. of ICALP'00. Springer, Lecture Notes in Comput. Sci. 1853 (2000) 536-546. CrossRef
E. Leiss, Language equations. Springer (1998).
M. Lothaire, Combinatorics on words. Addison-Wesley (1983).
A. Lentin and M.-P. Schützenberger, A combinatorial problem in the theory of free monoids, in Combinatorial Mathematics and its Applications. Univ. North Carolina Press (1969) 128-144.
Makanin, G.S., The problem of solvability of equations in a free semigroup. Mat. Sb. 103 (1977) 147-236 (English transl. in Math USSR Sb. 32 (1979) 129-198).
Perrin, D., Codes conjugués. Inform. and Control 20 (1972) 222-231. CrossRef
W. Plandowski, Satisfiability of word equations with constants is in PSPACE, in Proc. of FOCS'99. IEEE (1999) 495-500.
Ratoandramanana, B., Codes et motifs. RAIRO: Theoret. Informatics Appl. 23 (1989) 425-444.