We say that two languages and are conjugates if they satisfy the conjugacy equation for some language . We study several problems associated with this equation. For example, we characterize all sets which are conjugated a two-element biprefix set , as well as all two-element sets which are conjugates.
@article{ITA_2001__35_6_535_0, author = {Cassaigne, Julien and Karhum\"aki, Juhani and Ma\v nuch, J\'an}, title = {On conjugacy of languages}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {35}, year = {2001}, pages = {535-550}, mrnumber = {1922294}, zbl = {1005.68121}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2001__35_6_535_0} }
Cassaigne, Julien; Karhumäki, Juhani; Maňuch, Ján. On conjugacy of languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) pp. 535-550. http://gdmltest.u-ga.fr/item/ITA_2001__35_6_535_0/
[1] Combinatorics of words, in Handbook of Formal Languages, Vol. 1, edited by G. Rozenberg and A. Salomaa. Springer (1997) 329-438. | MR 1469998
and ,[2] The commutation of finite sets: A challenging problem. Theoret. Comput. Sci. 273 (2002) 69-79. | MR 1872443 | Zbl 1014.68128
, and ,[3] Regular algebra and finite machines. Chapman Hall (1971). | Zbl 0231.94041
,[4] Automata, languages and machines. Academic Press (1974). | Zbl 0317.94045
,[5] Independent systems of equations, Chap. 14 of Algebraic combinatorics on words, by M. Lothaire. Cambridge University Press (2002). | MR 1905123
, and ,[6] On commutation and primitive roots of codes. TUCS Technical Report 402 (2001).
and ,[7] Combinatorial and computational problems of finite sets of words, in Proc. of MCU'01. Springer, Lecture Notes in Comput. Sci. 2055 (2001) 69-81. | Zbl 0984.68118
,[8] On the centralizer of a finite set, in Proc. of ICALP'00. Springer, Lecture Notes in Comput. Sci. 1853 (2000) 536-546. | Zbl 0973.68115
and ,[9] Language equations. Springer (1998). | MR 1724110 | Zbl 0926.68064
,[10] Combinatorics on words. Addison-Wesley (1983). | MR 675953 | Zbl 0514.20045
,[11] A combinatorial problem in the theory of free monoids, in Combinatorial Mathematics and its Applications. Univ. North Carolina Press (1969) 128-144. | MR 251158 | Zbl 0221.20076
and ,[12] 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). | MR 470107 | Zbl 0396.20037
,[13] Codes conjugués. Inform. and Control 20 (1972) 222-231. | MR 345711 | Zbl 0254.94015
,[14] Satisfiability of word equations with constants is in PSPACE, in Proc. of FOCS'99. IEEE (1999) 495-500.
,[15] Codes et motifs. RAIRO: Theoret. Informatics Appl. 23 (1989) 425-444. | Numdam | MR 1036694 | Zbl 0689.68102
,