The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.
Mots-clés : periodic words, bi-ideals, the sequence generates the bi-ideal, finitely generated bi-ideals
@article{ITA_2008__42_3_467_0, author = {Buls, J\={a}nis and Lorencs, Aivars}, title = {From bi-ideals to periodicity}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {467--475}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/ita:2008010}, mrnumber = {2434029}, zbl = {1149.68410}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2008010/} }
TY - JOUR AU - Buls, Jānis AU - Lorencs, Aivars TI - From bi-ideals to periodicity JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 467 EP - 475 VL - 42 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2008010/ DO - 10.1051/ita:2008010 LA - en ID - ITA_2008__42_3_467_0 ER -
%0 Journal Article %A Buls, Jānis %A Lorencs, Aivars %T From bi-ideals to periodicity %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 467-475 %V 42 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2008010/ %R 10.1051/ita:2008010 %G en %F ITA_2008__42_3_467_0
Buls, Jānis; Lorencs, Aivars. From bi-ideals to periodicity. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 467-475. doi : 10.1051/ita:2008010. http://www.numdam.org/articles/10.1051/ita:2008010/
[1] Avoidable patterns in strings of symbols. Pacific J. Math. 85 (1979) 261-294. | MR | Zbl
, and .[2] Combinatorics on Words - A Tutorial. TUCS Technical Report (No. 530, June) (2003). | MR
, .[3] Une condition de finitude des monoïdes finiment engendrés. C.R. Acad. Sci. Paris, Sér. A 262 (1966) 1149-1151. | MR | Zbl
and .[4] Squares, cubes, and time-space efficient string searchinng. Algorithmica 13 (1995) 405-425. | MR | Zbl
and .[5] Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl
, . (1965)[6] Algorithms on Strings, Trees, and Sequences. Cambridge University Press (1997). | MR | Zbl
.[7] Structure of Rings. American Mathematical Society, Providence, RI (1964). | MR | Zbl
.[8] Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17. Addison-Wesley, Reading, Massachusetts (1983). | MR | Zbl
.[9] Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 90. Cambridge University Press, Cambridge (2002). | MR | Zbl
.[10] Finiteness and Regularity in Semigroups and Formal Languages. Springer-Verlag, Berlin, Heidelberg (1999). | MR | Zbl
.[11] Analysis and Design of Stream Ciphers. Springer-Verlag, Berlin (1986). | MR | Zbl
.[12] Infinite words and a theorem of Hindman. Rev. Math. Appl. 9 (1988) 97-104. | MR | Zbl
.[13] Data compression: methods and theory. Computer Science Press, Rockville, MD (1988).
.[14] Blocking sets of terms. Matem. sb., 119, 363-375 (Russian) (1982). | MR | Zbl
.Cité par Sources :