TY - GEN

T1 - Involutory Turing Machines

AU - Nakano, Keisuke

N1 - Funding Information:
Acknowledment. I am grateful to Robert Glück who has kindly lectured to me about reversible Turing machines and their expressiveness. I also thank Kanae Tsushima for her observation on the involutoriness of bidirectional transformation and Mirai Ikebuchi for carefully proofreading the manuscript. Furthermore, I want to appreciate anonymous reviewers’ fruitful comments on a close connection with time-symmetric machines. This work was partially supported by JSPS KAKENHI Grant Numbers JP17K00007, JP18H03204, and JP18H04093.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Bidirectional transformation language

KW - Involution

KW - Reversible Turing machine

KW - Time-symmetric machine

KW - Universal Turing machine

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U2 - 10.1007/978-3-030-52482-1_3

DO - 10.1007/978-3-030-52482-1_3

M3 - Conference contribution

AN - SCOPUS:85088583757

SN - 9783030524814

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 54

EP - 70

BT - Reversible Computation - 12th International Conference, RC 2020, Proceedings

A2 - Lanese, Ivan

A2 - Rawski, Mariusz

PB - Springer

T2 - 12th International Conference on Reversible Computation,RC 2020

Y2 - 9 July 2020 through 10 July 2020

ER -