The non-emptiness, called the Domino Problem, and the characterization of the possible entropies of 2 -subshifts of finite type are standard problems of symbolic dynamics. In this article we study these questions with horizontal constraints fixed beforehand as a parameter. We determine for which horizontal constraints the Domino Problem is undecidable and when all right-recursively enumerable numbers can be obtained as entropy, with two approaches: either the additional local rules added to the horizontal constraints can be of any shape, or they can only be vertical rules.Note that a Rauzy graph can be made of one or several strongly connected components (SCC for short). We recall that it is constituted of one unique strongly connected components if and only if the SFT associated is transitive; that is, for any u, w ∈ L H there exists v ∈ L H so that uvw ∈ L H . If the Rauzy graph has several SCCs it can also contain transient vertices, that are vertices with no path from themselves to themselves. We refer to [LM95] for more details.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.