Abstract
Purchase PDF (312 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (3)
Purchase PDF (1416 K)
doi:10.1016/j.tcs.2004.02.018 
Copyright © 2004 Elsevier B.V. All rights reserved.
Quasi-periodic configurations and undecidable dynamics for tilings, infinite words and Turing machines
Available online 7 March 2004.
References and further reading may be available for this article. To view references and further reading you must purchase this article.
Abstract
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 always have periodic configurations; we prove that they always have quasi-periodic configurations 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.
Author Keywords: Tiling; Turing machine; Dynamical systems; Undecidability; Quasi-periodicity
