From bi-ideals to periodicity
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 467-475.

The necessary and sufficient conditions are extracted for periodicity of bi-ideals. They cover infinitely and finitely generated bi-ideals.

DOI: 10.1051/ita:2008010
Classification: 68R15,  94A55,  68Q15
Keywords: periodic words, bi-ideals, the sequence generates the bi-ideal, finitely generated bi-ideals
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Buls, Jānis; Lorencs, Aivars. From bi-ideals to periodicity. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 467-475. doi : 10.1051/ita:2008010. http://www.numdam.org/articles/10.1051/ita:2008010/

[1] D.B. Bean, A.E. Ehrenfeucht and G. Mcnulty. Avoidable patterns in strings of symbols. Pacific J. Math. 85 (1979) 261-294. | MR | Zbl

[2] J. Berstel, J. Karhumäki. Combinatorics on Words - A Tutorial. TUCS Technical Report (No. 530, June) (2003). | MR

[3] M. Coudrain and M.P. Schützenberger. Une condition de finitude des monoïdes finiment engendrés. C.R. Acad. Sci. Paris, Sér. A 262 (1966) 1149-1151. | MR | Zbl

[4] M. Crochemore and W. Rytter. Squares, cubes, and time-space efficient string searchinng. Algorithmica 13 (1995) 405-425. | MR | Zbl

[5] N.J. Fine, H.S. Wilf. (1965) Uniqueness theorem for periodic functions. Proc. Amer. Math. Soc. 16 (1965) 109-114. | MR | Zbl

[6] D. Gusfield. Algorithms on Strings, Trees, and Sequences. Cambridge University Press (1997). | MR | Zbl

[7] N. Jacobson. Structure of Rings. American Mathematical Society, Providence, RI (1964). | MR | Zbl

[8] M. Lothaire. Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 17. Addison-Wesley, Reading, Massachusetts (1983). | MR | Zbl

[9] M. Lothaire. Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, Vol. 90. Cambridge University Press, Cambridge (2002). | MR | Zbl

[10] Aldo De Luca, Stefano Varricchio. Finiteness and Regularity in Semigroups and Formal Languages. Springer-Verlag, Berlin, Heidelberg (1999). | MR | Zbl

[11] R.A. Rueppel. Analysis and Design of Stream Ciphers. Springer-Verlag, Berlin (1986). | MR | Zbl

[12] I. Simon. Infinite words and a theorem of Hindman. Rev. Math. Appl. 9 (1988) 97-104. | MR | Zbl

[13] J.A. Storer. Data compression: methods and theory. Computer Science Press, Rockville, MD (1988).

[14] A.I. Zimin. Blocking sets of terms. Matem. sb., 119, 363-375 (Russian) (1982). | MR | Zbl

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