Minimal entropy approximation for cellular automata
نویسندگان
چکیده
منابع مشابه
Entropy of Cellular Automata
Let X = S where G is a countable group and S is a finite set. A cellular automaton (CA) is an endomorphism T : X → X (continuous, commuting with the action of G). Shereshevsky [13] proved that for G = Z with d > 1 no CA can be forward expansive, raising the following conjecture: For G = Z, d > 1 the topological entropy of any CA is either zero or infinite. Morris and Ward [10], proved this for ...
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Let X = S where G is a countable group and S is a finite set. A cellular automaton (CA) is an endomorphism T : X → X (continuous, commuting with the action of G). Shereshevsky [14] proved that for G = Z with d > 1 no CA can be forward expansive, raising the following conjecture: For G = Z, d > 1 the topological entropy of any CA is either zero or infinite. Morris and Ward [11], proved this for ...
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A radius-r one-dimensional cellular automaton (CA) is an infinite sequence of identical finite-state machines (indexed by Ÿ) called cells. Each finite-state machine is in a state and these states change simultaneously according to a local transition function: the following state of the machine is related to its own state as well as the states of its 2r neighbors. A configuration of an automaton...
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We study the topological entropy of a particular class of dynamical systems: cellular automata. The topological entropy of a dynamical system (X; F) is a measure of the complexity of the dynamics of F over the space X . The problem of computing (or even approximating) the topological entropy of a given cellular automata is algorithmically undecidable (Ergodic Theory Dynamical Systems 12 (1992) ...
متن کاملEntropy rate of higher-dimensional cellular automata
We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift–commuting isomorphisms; as opposed to the entropy of such CA, it is always finite. The invariance property and the finiteness of the entropy rate result from basic results about the entropy of partitions of multidimensional cellular automata. We prove several results that show that entropy ...
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ژورنال
عنوان ژورنال: Journal of Statistical Mechanics: Theory and Experiment
سال: 2014
ISSN: 1742-5468
DOI: 10.1088/1742-5468/2014/02/p02009