Polynomial languages with finite antidictionaries
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 269-279.

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.

DOI : 10.1051/ita:2008028
Classification : 68Q45, 68R15
Mots-clés : regular language, finite antidictionary, combinatorial complexity, wed-like automaton 
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     title = {Polynomial languages with finite antidictionaries},
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Shur, Arseny M. Polynomial languages with finite antidictionaries. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 269-279. doi : 10.1051/ita:2008028. http://www.numdam.org/articles/10.1051/ita:2008028/

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

[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

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

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

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

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

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