3,205 research outputs found
Characterization for entropy of shifts of finite type on Cayley trees
The notion of tree-shifts constitutes an intermediate class in between
one-sided shift spaces and multidimensional ones. This paper proposes an
algorithm for computing of the entropy of a tree-shift of finite type.
Meanwhile, the entropy of a tree-shift of finite type is for some , where is a Perron number. This
extends Lind's work on one-dimensional shifts of finite type. As an
application, the entropy minimality problem is investigated, and we obtain the
necessary and sufficient condition for a tree-shift of finite type being
entropy minimal with some additional conditions
Some properties of topological pressure on cellular automata
This paper investigates the ergodicity and the power rule of the topological pressure of a cellular automaton. If a cellular automaton is either leftmost or rightmost premutive (due to the terminology given by Hedlund [Math.~Syst.~Theor.~3, 320-375, 1969]), then it is ergodic with respect to the uniform Bernoulli measure. More than that, the relation of topological pressure between the original cellular automaton and its power rule is expressed in a closed form. As an application, the topological pressure of a linear cellular automaton can be computed explicitly
- …