no. 3
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.

DOI : 10.1051/ita:2008021
Classification : 68Q70, 68R15 
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     title = {Comparing complexity functions of a language and its extendable part},
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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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

[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 | MR

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

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

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