Gardens of Eden and amenability on cellular automata
Laurent Bartholdi (2010)
Journal of the European Mathematical Society
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Laurent Bartholdi (2010)
Journal of the European Mathematical Society
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Gorbulsky, A.D. (2005)
Zapiski Nauchnykh Seminarov POMI
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Prasanna K. Sahoo (1986)
Kybernetika
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Fumio Hiai, Dénes Petz (2007)
Banach Center Publications
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A new expression as a certain asymptotic limit via "discrete micro-states" of permutations is provided for the mutual information of both continuous and discrete random variables.
Dajani, Karma, Meester, Ronald (2003)
International Journal of Mathematics and Mathematical Sciences
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Ludwig Staiger (2010)
RAIRO - Theoretical Informatics and Applications
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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.
L. Salce, P. Zanardo (2010)
Colloquium Mathematicae
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The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of...
Christoph Schwab, Svetlana Tokareva (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We analyze the regularity of random entropy solutions to scalar hyperbolic conservation laws with random initial data. We prove regularity theorems for statistics of random entropy solutions like expectation, variance, space-time correlation functions and polynomial moments such as gPC coefficients. We show how regularity of such moments (statistical and polynomial chaos) of random entropy solutions depends on the regularity of the distribution law of the random shock location of the...
R. C. Carrasco (1997)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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V. Gundlach, G. Ochs (2000)
Colloquium Mathematicae
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We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.
Cutler, Jonathan, Radcliffe, A.J. (2011)
The Electronic Journal of Combinatorics [electronic only]
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Mika Hirvensalo, Sebastian Seibert (2003)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language is accepted by a Las Vegas automaton having states such that the probability for a definite answer to occur is at least , then , where is the number of the states of the minimal deterministic automaton accepting . Earlier this result has been obtained in [2] by using...