# The Group of Reversible Turing Machines

2 MC2 - Modèles de calcul, Complexité, Combinatoire
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We consider Turing machines as actions over configurations in ${\Sigma }^{{\mathbb{Z}}^{d}}$which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines and the group of reversible Turing machines. We also study two natural subgroups, namely the group of finite-state automata, which generalizes the topological full groups studied in the theory of orbit-equivalence, and the group of oblivious Turing machines whose movement is independent of tape contents, which generalizes lamplighter groups and has connections to the study of universal reversible logical gates. Our main results are that the group of Turing machines in one dimension is neither amenable nor residually finite, but is locally embeddable in finite groups, and that the torsion problem is decidable for finite-state automata in dimension one, but not in dimension two.
Document type :
Conference papers
Domain :

Cited literature [29 references]

https://hal.inria.fr/hal-01435034
Contributor : Hal Ifip <>
Submitted on : Friday, January 13, 2017 - 3:24:06 PM
Last modification on : Wednesday, May 6, 2020 - 8:18:02 PM
Long-term archiving on: : Friday, April 14, 2017 - 7:08:49 PM

### File

395687_1_En_5_Chapter.pdf
Files produced by the author(s)

### Citation

Sebastián Barbieri, Jarkko Kari, Ville Salo. The Group of Reversible Turing Machines. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. pp.49-62, ⟨10.1007/978-3-319-39300-1_5⟩. ⟨hal-01435034⟩

Record views