A Small Minimal Aperiodic Reversible Turing Machine

Abstract : A simple reversible Turing machine with four states, three symbols and no halting configuration is constructed that has no periodic orbit, simplifying a construction by Blondel, Cassaigne and Nichitiu and positively answering a conjecture by Kari and Ollinger. The constructed machine has other interesting properties: it is symmetric both for space and time and has a topologically minimal associated dynamical system whose column shift is associated to a substitution. Using a particular embedding technique of an arbitrary reversible Turing machine into the one presented, it is proven that the problem of determining if a given reversible Turing machine without halting state has a periodic orbit is undecidable.
Type de document :
Article dans une revue
Journal of Computer and System Sciences (JCSS), Elsevier, 2017, 84, pp.288-301. 〈http://dx.doi.org/10.1016/j.jcss.2016.10.004〉
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00975244
Contributeur : Nicolas Ollinger <>
Soumis le : mardi 8 avril 2014 - 11:40:10
Dernière modification le : lundi 4 mars 2019 - 14:04:18
Document(s) archivé(s) le : mardi 8 juillet 2014 - 11:30:49

Fichier

smart.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00975244, version 1

Citation

Julien Cassaigne, Nicolas Ollinger, Rodrigo Torres. A Small Minimal Aperiodic Reversible Turing Machine. Journal of Computer and System Sciences (JCSS), Elsevier, 2017, 84, pp.288-301. 〈http://dx.doi.org/10.1016/j.jcss.2016.10.004〉. 〈hal-00975244〉

Partager

Métriques

Consultations de la notice

494

Téléchargements de fichiers

5892