Quasi-periodic configurations and undecidable dynamics for tilings, infinite words and Turing machines
نویسندگان
چکیده
We describe Turing machines, tilings and in#nite words as dynamical systems and analyze some of their dynamical properties. It is known that some of these systems do not always have periodic con#gurations; we prove that they always have quasi-periodic con#gurations and we quantify quasi-periodicity. We then study the decidability of dynamical properties for these systems. In analogy to Rice’s theorem for computable functions, we derive a theorem that characterizes dynamical system properties that are undecidable. As an illustration of this result, we prove that topological entropy is undecidable for Turing machines and for tilings. c © 2004 Elsevier B.V. All rights reserved.
منابع مشابه
Dynamics, Information and Computation
Structure of the thesis The heart of this thesis is composed of four independent chapters, related by a common flavor of systems theory and computer science. Chapter 3: Almost periodic configurations and undecidable dynamics. We describe Turing machines, tilings and infinite words as dynamical systems and analyze some of their dynamical properties. It is known that some of these systems do not ...
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 319 شماره
صفحات -
تاریخ انتشار 2004