Involutory Turing Machines

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Citations (Scopus)


An involutory function, also called involution, is a function that is its own inverse, i.e., holds whenever is defined. This paper presents a computational model of involution as a variant of Turing machines, called an involutory Turing machine. The computational model is shown to be complete in the sense that not only does an involutory Turing machine always compute an involution but also every involutory computable function can be computed by an involutory Turing machine. As any involution is injective (hence reversible), any involutory Turing machine forms a standard reversible Turing machine that is backward deterministic. Furthermore, the existence of a universal involutory Turing machine is shown under an appropriate redefinition of universality given by Axelsen and Glück for reversible Turing machines. This work is motivated by characterizing bidirectional transformation languages.

Original languageEnglish
Title of host publicationReversible Computation - 12th International Conference, RC 2020, Proceedings
EditorsIvan Lanese, Mariusz Rawski
Number of pages17
ISBN (Print)9783030524814
Publication statusPublished - 2020
Event12th International Conference on Reversible Computation,RC 2020 - Oslo, Norway
Duration: 2020 Jul 92020 Jul 10

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12227 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th International Conference on Reversible Computation,RC 2020


  • Bidirectional transformation language
  • Involution
  • Reversible Turing machine
  • Time-symmetric machine
  • Universal Turing machine


Dive into the research topics of 'Involutory Turing Machines'. Together they form a unique fingerprint.

Cite this