Tree-shifts: the entropy of tree-shifts of finite type
نویسندگان
چکیده
منابع مشابه
Tree-shifts of finite type
A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type de...
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A one-sided (resp. two-sided) shift of finite type of dimension one can be described as the set of infinite (resp. bi-infinite) sequences of consecutive edges in a finite-state automaton. While the conjugacy of shifts of finite type is decidable for one-sided shifts of finite type of dimension one, the result is unknown in the two-sided case. In this paper, we study the shifts of finite type de...
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We introduce the notion of sofic tree-shifts which corresponds to symbolic dynamical systems of infinite trees accepted by finite tree automata. We show that, contrary to shifts of infinite sequences, there is no unique minimal deterministic irreducible tree automaton accepting an irreducible sofic tree-shift, but that there is a unique synchronized one, called the Shannon cover of the tree-shi...
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Any higher dimensional shift space (X, d) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of d where r < d. We show here that any projectional entropy is bounded below by the d entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite p...
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For any fixed alphabet A, the maximum topological entropy of a Z d subshift with alphabet A is obviously log |A|. We study the class of nearest neighbor Z shifts of finite type which have topological entropy very close to this maximum, and show that they have many useful properties. Specifically, we prove that for any d, there exists δd > 0 such that for any nearest neighbor Z d shift of finite...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2017
ISSN: 0951-7715,1361-6544
DOI: 10.1088/1361-6544/aa72c0