Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Conference papers

The Group of Reversible Turing Machines

Abstract : We consider Turing machines as actions over configurations in Σ 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
Complete list of metadata

Cited literature [29 references]  Display  Hide  Download
Contributor : Hal Ifip Connect in order to contact the contributor
Submitted on : Friday, January 13, 2017 - 3:24:06 PM
Last modification on : Saturday, September 11, 2021 - 3:17:28 AM
Long-term archiving on: : Friday, April 14, 2017 - 7:08:49 PM


Files produced by the author(s)


Distributed under a Creative Commons Attribution 4.0 International License



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


Files downloads