Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T07:13:52.349Z Has data issue: false hasContentIssue false
  • English
  • Français

The entropy of Łukasiewicz-languages

Published online by Cambridge University Press:  15 October 2005

Ludwig Staiger
Ludwig Staiger*
Affiliation:
Martin-Luther-Universität Halle-Wittenberg, Institut für Informatik, von-Seckendorff-  Platz 1, D–06099 Halle (Saale), Germany; staiger@informatik.uni-halle.de
Get access

Abstract

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.

Keywords

Entropy of languagesBernoulli measure of languagescodesŁukasiewicz language
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 4 , October 2005 , pp. 621 - 639
Copyright
© EDP Sciences, 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.
J. Berstel and D. Perrin, Theory of Codes. Academic Press, Orlando (1985).
Chomsky, N. and Miller, G.A., Finite-state languages. Inform. Control 1 (1958) 91–112. CrossRef
Devolder, J., Latteux, M., Litovski, I. and Staiger, L., Infinite Words, Codes. Acta Cybernetica 11 (1994) 241–256.
S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press, New York (1974).
Fernau, H., Valuations of Languages, with Applications to Fractal Geometry. Theoret. Comput. Sci. 137 (1995) 177–217. CrossRef
Hansel, G., Perrin, D. and Simon, I., Entropy and compression, in STACS'92, edited by A. Finkel and M. Jantzen. Lect. Notes Comput. Sci. 577 (1992) 515–530.
R. Johannesson, Informations theorie. Addison-Wesley (1992).
Justesen, J. and Larsen, K., Probabilistic Context-Free Grammars, On that Achieve Capacity. Inform. Control 29 (1975) 268–285. CrossRef
Kaminger, F.P., The noncomputability of the channel capacity of context-sensitive languages. Inform. Control 17 (1970) 175–182. CrossRef
Kuich, W., On the entropy of context-free languages. Inform. Control 16 (1970) 173–200. CrossRef
M. Li and P.M.B. Vitányi, An Introduction to Kolmogorov Complexity and its Applications. Springer-Verlag, New York (1993).
Staiger, L., On infinitary finite length codes. RAIRO-Inf. Theor. Appl. 20 (1986) 483–494. CrossRef
Staiger, L., Ein Satz über die Entropie von Untermonoiden. Theor. Comput. Sci. 61 (1988) 279–282. CrossRef
Staiger, L., Kolmogorov complexity and Hausdorff dimension. Inform. Comput. 103 (1993) 159–194. CrossRef