Polynomial languages with finite antidictionaries
Shur, Arseny M.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009), p. 269-279 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.

Publié le : 2009-01-01
DOI : https://doi.org/10.1051/ita:2008028
Classification:  68Q45,  68R15 
@article{ITA_2009__43_2_269_0,
     author = {Shur, Arseny M.},
     title = {Polynomial languages with finite antidictionaries},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {43},
     year = {2009},
     pages = {269-279},
     doi = {10.1051/ita:2008028},
     mrnumber = {2512259},
     zbl = {1166.68026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2009__43_2_269_0}
}

Shur, Arseny M. Polynomial languages with finite antidictionaries. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) pp. 269-279. doi : 10.1051/ita:2008028. http://gdmltest.u-ga.fr/item/ITA_2009__43_2_269_0/

[1] F.-J. Brandenburg, Uniformly growing k-th power free homomorphisms. Theoret. Comput. Sci. 23 (1983) 69-82. | MR 693069 | Zbl 0508.68051

[2] C. Choffrut and J. Karhumäki, Combinatorics of words, in Handbook of formal languages, Vol. 1, Chap. 6, edited by G. Rosenberg, A. Salomaa. Springer, Berlin (1997), 329-438. | MR 1469998

[3] M. Crochemore, F. Mignosi and A. Restivo, Automata and forbidden words. Inform. Process. Lett. 67 (1998) 111-117. | MR 1638178

[4] A. Ehrenfeucht and G. Rozenberg, On subword complexities of homomorphic images of languages. RAIRO-Theor. Inf. Appl. 16 (1982) 303-316. | Numdam | MR 707633 | Zbl 0495.68069

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

[6] A.M. Shur, Combinatorial complexity of rational languages. Discr. Anal. Oper. Res., Ser. 1 12 (2005) 78-99 (in Russian). | MR 2168157 | Zbl 1249.68107