On the presence of periodic configurations in Turing machines and in counter machines

Authors:
Vincent D. Blondel;Julien Cassaigne;Codrin Nichitiu
Affiliations:
Division of Applied Mathematics, Center Cesame, Université catholique de Louvain, 4 avenue Georges Lemaitre, B-1348 Louvain-la-Neuve, Belgium;Institut de Mathématiques de Luminy--CNRS, 163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France;EURISE, Université Jean Monnet St Étienne, 23, rue du Dr Paul Michelon, 42023 St Étienne Cedex 2, France
Venue:
Theoretical Computer Science
Year:
2002

Citing 5
Cited 10

On topological dynamics of Turing machines

Theoretical Computer Science
Deciding stability and mortality of piecewise affine dynamical systems

Theoretical Computer Science
The stability of saturated linear dynamical systems is undecidable

Journal of Computer and System Sciences
Formal languages and their relation to automata

Formal languages and their relation to automata
Automata Studies. (AM-34) (Annals of Mathematics Studies)

Automata Studies. (AM-34) (Annals of Mathematics Studies)

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

Theoretical Computer Science - Combinatorics of the discrete plane and tilings
One Head Machines from a symbolic approach

Theoretical Computer Science
Periodicity and Immortality in Reversible Computing

MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the Computational Power of Querying the History

Fundamenta Informaticae - Machines, Computations and Universality, Part II
Periodic and infinite traces in matrix semigroups

SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
The most general conservation law for a cellular automaton

CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Note: The periodic domino problem revisited

Theoretical Computer Science
Zigzags in turing machines

CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
On the Computational Power of Querying the History

Fundamenta Informaticae - Machines, Computations and Universality, Part II
On immortal configurations in turing machines

CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes

Quantified Score

Hi-index	5.23

Visualization

Abstract

A configuration of a Turing machine is given by a tape content together with a particular state of the machine. Petr Kůrka has conjectured that every Turing machine--when seen as a dynamical system on the space of its configurations--has at least one periodic orbit. In this paper, we provide an explicit counterexample to this conjecture. We also consider counter machines and prove that, in this case, the problem of determining if a given machine has a periodic orbit in configuration space is undecidable.