On the Computability of the Topological Entropy of Subshifts
نویسنده
چکیده
We prove that the topological entropy of subshifts having decidable language is uncomputable in the following sense: For no error bound less than 1/4 does there exists a program that, given a decision procedure for the language of a subshift as input, will approximate the entropy of the subshift within the error bound. In addition, we prove that not only is the topological entropy of sofic shifts computable to arbitary precision (a well-known fact), but all standard comparisons of the topological entropy with rational numbers are decidable.
منابع مشابه
Computing the entropy of one-dimensional decidable subshifts
We characterise the difficulty of computing topological entropy of one-dimensional subshifts under various dynamical restrictions. Entropy is known to be computable from above for general one-dimensional subshifts, and the aim of the article is to distinguish under which dynamical properties it becomes computable. The considered properties are minimality, unique ergodicity, and various forms of...
متن کاملha o - dy n / 99 10 00 3 v 1 3 O ct 1 99 9 Chaotic Properties of Subshifts Generated by a Non - Periodic Recurrent Orbit July 1999 Xin -
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions...
متن کاملA Class of Simple C-algebras Arising from Certain Nonsofic Subshifts
We present a class of subshifts ZN , N = 1, 2, . . . whose associated C∗-algebras OZN are simple, purely infinite and not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The class of the subshifts is the first examples whose associated C∗-algebras are not stably isomorphic to any Cuntz-Krieger algebra nor to Cuntz algebra. The subshifts ZN are coded systems whose languages ...
متن کاملRow Subshifts and Topological Entropy of Cellular Automata
Cellular Automata (CA) are symbolic dynamical systems often used in computer science as models of complex systems [9]. The topological entropy is often referred to as a measure of the complexity of a dynamical system [1]. The topological entropy of a CA (AZ, F ) is defined in terms of the entropy of its column subshifts Σk [4], H(F ) = limk→∞ H(Σk) k . Here we address the following question: is...
متن کاملImplications of Mixing Properties on Intrinsic Ergodicity in Symbolic Dynamics
We study various mixing properties for subshifts, which allow words in the language to be concatenated into a new word in the language given certain gaps between them. All are defined in terms of an auxiliary gap function f : N → N, which gives the minimum required gap length as a function of the lengths of the words on either side. In this work we focus mostly on topological transitivity, topo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics & Theoretical Computer Science
دوره 8 شماره
صفحات -
تاریخ انتشار 2006