Quasi-periodic configurations and undecidable dynamics for tilings, infinite words and turing machines

Authors:
Jean-Charles Delvenne;Vincent D. Blondel
Affiliations:
Division of Applied Mathematics, Unversité Catholique de Louvain, 4 Avenue Georges Lemaître, Louvain-la-Neuve B-1348, Belgium;Division of Applied Mathematics, Unversité Catholique de Louvain, 4 Avenue Georges Lemaître, Louvain-la-Neuve B-1348, Belgium
Venue:
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Year:
2004

Citing 6
Cited 4

Rice's theorem for the limit sets of cellular automata

Theoretical Computer Science
An aperiodic set of 13 Wang tiles

Discrete Mathematics
On topological dynamics of Turing machines

Theoretical Computer Science
Tilings and quasiperiodicity

Theoretical Computer Science
Strong cocycle triviality for ***2 shushifts

Theoretical Computer Science
On the presence of periodic configurations in Turing machines and in counter machines

Theoretical Computer Science

Decidability and Universality in Symbolic Dynamical Systems

Fundamenta Informaticae - SPECIAL ISSUE MCU2004
On beta-shifts having arithmetical languages

MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
On immortal configurations in turing machines

CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Decidability and Universality in Symbolic Dynamical Systems

Fundamenta Informaticae - SPECIAL ISSUE MCU2004

Quantified Score

Hi-index	0.00

Visualization

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.