The entropy of Łukasiewicz-languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 4, pp. 621-639.

The paper presents an elementary approach for the calculation of the entropy of a class of languages. This approach is based on the consideration of roots of a real polynomial and is also suitable for calculating the Bernoulli measure. The class of languages we consider here is a generalisation of the Łukasiewicz language.

DOI : 10.1051/ita:2005032
Classification : 68Q30, 68Q45, 94A17
Mots-clés : entropy of languages, Bernoulli measure of languages, codes, Łukasiewicz language
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Staiger, Ludwig. The entropy of Łukasiewicz-languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 4, pp. 621-639. doi : 10.1051/ita:2005032. http://archive.numdam.org/articles/10.1051/ita:2005032/

[1] J.-M. Autebert, J. Berstel and L. Boasson, Context-Free Languages and Pushdown Automata, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Springer-Verlag, Berlin 1 (1997) 111-174.

[2] J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985). | MR | Zbl

[3] N. Chomsky and G.A. Miller, Finite-state languages. Inform. Control 1 (1958) 91-112. | Zbl

[4] J. Devolder, M. Latteux, I. Litovski and L. Staiger, Codes and Infinite Words. Acta Cybernetica 11 (1994) 241-256. | Zbl

[5] S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press, New York (1974). | MR | Zbl

[6] H. Fernau, Valuations of Languages, with Applications to Fractal Geometry. Theoret. Comput. Sci. 137 (1995) 177-217. | Zbl

[7] G. Hansel, D. Perrin and I. Simon, Entropy and compression, in STACS'92, edited by A. Finkel and M. Jantzen. Lect. Notes Comput. Sci. 577 (1992) 515-530.

[8] R. Johannesson, Informations theorie. Addison-Wesley (1992).

[9] J. Justesen and K. Larsen, On Probabilistic Context-Free Grammars that Achieve Capacity. Inform. Control 29 (1975) 268-285. | Zbl

[10] F.P. Kaminger, The noncomputability of the channel capacity of context-sensitive languages. Inform. Control 17 (1970) 175-182. | Zbl

[11] W. Kuich, On the entropy of context-free languages. Inform. Control 16 (1970) 173-200. | Zbl

[12] M. Li and P.M.B. Vitányi, An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag, New York (1993). | MR | Zbl

[13] L. Staiger, On infinitary finite length codes. RAIRO-Inf. Theor. Appl. 20 (1986) 483-494. | EuDML | Numdam | Zbl

[14] L. Staiger, Ein Satz über die Entropie von Untermonoiden. Theor. Comput. Sci. 61 (1988) 279-282. | Zbl

[15] L. Staiger, Kolmogorov complexity and Hausdorff dimension. Inform. Comput. 103 (1993) 159-194. | Zbl

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