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.
Mots-clés : entropy of languages, Bernoulli measure of languages, codes, Łukasiewicz language
@article{ITA_2005__39_4_621_0, author = {Staiger, Ludwig}, title = {The entropy of {{\L}ukasiewicz-languages}}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {621--639}, publisher = {EDP-Sciences}, volume = {39}, number = {4}, year = {2005}, doi = {10.1051/ita:2005032}, zbl = {1073.68670}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita:2005032/} }
TY - JOUR AU - Staiger, Ludwig TI - The entropy of Łukasiewicz-languages JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 621 EP - 639 VL - 39 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2005032/ DO - 10.1051/ita:2005032 LA - en ID - ITA_2005__39_4_621_0 ER -
%0 Journal Article %A Staiger, Ludwig %T The entropy of Łukasiewicz-languages %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 621-639 %V 39 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2005032/ %R 10.1051/ita:2005032 %G en %F ITA_2005__39_4_621_0
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://www.numdam.org/articles/10.1051/ita:2005032/
[1] 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.
, and ,[2] Theory of Codes. Academic Press, Orlando (1985). | MR | Zbl
and ,[3] Finite-state languages. Inform. Control 1 (1958) 91-112. | Zbl
and ,[4] Codes and Infinite Words. Acta Cybernetica 11 (1994) 241-256. | Zbl
, , and ,[5] Automata, Languages and Machines, Vol. A. Academic Press, New York (1974). | MR | Zbl
,[6] Valuations of Languages, with Applications to Fractal Geometry. Theoret. Comput. Sci. 137 (1995) 177-217. | Zbl
,[7] Entropy and compression, in STACS'92, edited by A. Finkel and M. Jantzen. Lect. Notes Comput. Sci. 577 (1992) 515-530.
, and ,[8] Informations theorie. Addison-Wesley (1992).
,[9] On Probabilistic Context-Free Grammars that Achieve Capacity. Inform. Control 29 (1975) 268-285. | Zbl
and ,[10] The noncomputability of the channel capacity of context-sensitive languages. Inform. Control 17 (1970) 175-182. | Zbl
,[11] On the entropy of context-free languages. Inform. Control 16 (1970) 173-200. | Zbl
,[12] An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag, New York (1993). | MR | Zbl
and ,[13] On infinitary finite length codes. RAIRO-Inf. Theor. Appl. 20 (1986) 483-494. | EuDML | Numdam | Zbl
,[14] Ein Satz über die Entropie von Untermonoiden. Theor. Comput. Sci. 61 (1988) 279-282. | Zbl
,[15] Kolmogorov complexity and Hausdorff dimension. Inform. Comput. 103 (1993) 159-194. | Zbl
,Cité par Sources :