Comparing complexity functions of a language and its extendable part
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 647-655.

Right (left, two-sided) extendable part of a language consists of all words having infinitely many right (resp. left, two-sided) extensions within the language. We prove that for an arbitrary factorial language each of these parts has the same growth rate of complexity as the language itself. On the other hand, we exhibit a factorial language which grows superpolynomially, while its two-sided extendable part grows only linearly.

@article{ITA_2008__42_3_647_0,
     author = {Shur, Arseny M.},
     title = {Comparing complexity functions of a language and its extendable part},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {647--655},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {3},
     year = {2008},
     doi = {10.1051/ita:2008021},
     zbl = {1149.68055},
     mrnumber = {2434040},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita:2008021/}
}
TY  - JOUR
AU  - Shur, Arseny M.
TI  - Comparing complexity functions of a language and its extendable part
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2008
DA  - 2008///
SP  - 647
EP  - 655
VL  - 42
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ita:2008021/
UR  - https://zbmath.org/?q=an%3A1149.68055
UR  - https://www.ams.org/mathscinet-getitem?mr=2434040
UR  - https://doi.org/10.1051/ita:2008021
DO  - 10.1051/ita:2008021
LA  - en
ID  - ITA_2008__42_3_647_0
ER  - 
Shur, Arseny M. Comparing complexity functions of a language and its extendable part. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 3, pp. 647-655. doi : 10.1051/ita:2008021. http://www.numdam.org/articles/10.1051/ita:2008021/

[1] C. Choffrut and J. Karhumäki, Combinatorics of words, in Handbook of formal languages 1, edited by G. Rosenberg, A. Salomaa. Springer, Berlin (1997) 329-438. | MR 1469998

[2] D.M. Cvetković, M. Doob and H. Sachs, Spectra of graphs. Theory and applications, 3rd edn. Johann Ambrosius Barth, Heidelberg (1995). | MR 1324340 | Zbl 0824.05046

[3] F. D'Alessandro, B. Intrigila and S. Varricchio, On the structure of counting function of sparse context-free languages. Theor. Comput. Sci. 356 (2006) 104-117. | MR 2217830 | Zbl 1160.68407

[4] A. Ehrenfeucht and G. Rozenberg, A limit theorem for sets of subwords in deterministic TOL languages. Inform. Process. Lett. 2 (1973) 70-73. | MR 323162 | Zbl 0299.68044

[5] F.R. Gantmacher, Application of the theory of matrices. Interscience, New York (1959). | MR 107648 | Zbl 0085.01001

[6] O. Ibarra and B. Ravikumar, On sparseness, ambiguity and other decision problems for acceptors and transducers. Lect. Notes Comput. Sci. 210 (1986) 171-179. | MR 827734 | Zbl 0605.68080

[7] Y. Kobayashi, Repetition-free words. Theor. Comput. Sci. 44 (1986) 175-197. | MR 860554 | Zbl 0596.20058

[8] Y. Kobayashi, Enumeration of irreducible binary words. Discrete Appl. Math. 20 (1988) 221-232. | MR 944122 | Zbl 0673.68046

[9] A. Lepistö, A characterization of 2 + -free words over a binary alphabet. Turku Centre for Computer Science, TUCS Tech. Report 74 (1996).

[10] M. Morse and G.A. Hedlund, Symbolic dynamics. Amer. J. Math. 60 (1938) 815-866. | JFM 64.0798.04 | MR 1507944

[11] A.M. Shur, Combinatorial complexity of rational languages. Discrete Anal. Oper. Res. 1 12 (2005) 78-99 (Russian). | MR 2168157

[12] A.M. Shur, On intermediate factorial languages. Turku Centre for Computer Science, TUCS Tech. Report 723 (2005). | MR 2168157

Cité par Sources :