RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Guidelines for authors Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Probl. Peredachi Inf.: Year: Volume: Issue: Page: Find

 Probl. Peredachi Inf., 2006, Volume 42, Issue 1, Pages 43–51 (Mi ppi36)

Automata Theory

Entropy of Multidimensional Cellular Automata

E. L. Lakshtanova, E. S. Langvagenb

a University of Aveiro
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Since the topological entropy of a vast class of two-dimensional cellular automata (CA) is infinite, of interest is the possibility to renormalize it so that to obtain a positive finite value. We find the asymptotics of the information function of a multidimensional CA and, accordingly, introduce the renormalized topological entropy as a coefficient of this asymptotics. We describe some properties of the introduced quantity, in particular, its positivity for CA of the type of “The Game of Life.” Also, we give an example of an explicit evaluation of this parameter for a particular cellular automaton.

Full text: PDF file (872 kB)
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2006, 42:1, 38–45

Bibliographic databases:

UDC: 621.391.1:519.27
Revised: 01.12.2005

Citation: E. L. Lakshtanov, E. S. Langvagen, “Entropy of Multidimensional Cellular Automata”, Probl. Peredachi Inf., 42:1 (2006), 43–51; Problems Inform. Transmission, 42:1 (2006), 38–45

Citation in format AMSBIB
\Bibitem{LakLan06} \by E.~L.~Lakshtanov, E.~S.~Langvagen \paper Entropy of Multidimensional Cellular Automata \jour Probl. Peredachi Inf. \yr 2006 \vol 42 \issue 1 \pages 43--51 \mathnet{http://mi.mathnet.ru/ppi36} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2214511} \zmath{https://zbmath.org/?q=an:1104.37009} \transl \jour Problems Inform. Transmission \yr 2006 \vol 42 \issue 1 \pages 38--45 \crossref{https://doi.org/10.1134/S0032946006010042} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33646013900}