Academic Journal

The group of reversible turing machines: subgroups, generators, and computability – CORRIGENDUM.

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Τίτλος: The group of reversible turing machines: subgroups, generators, and computability – CORRIGENDUM.
Πηγή: Forum of Mathematics, Sigma; 2025, Vol. 13, p1-42, 42p
Θεματικοί όροι: Turing machines, Reversible computing, Program generators (Computer programs), Subgroup analysis (Experimental design), Finite state machines, Recursion theory
Περίληψη: The article focuses on the study of an abstract group of reversible Turing machines, exploring their subgroups, generators, and computability aspects. It identifies three significant subgroups: the group of finite-state automata, the group of oblivious Turing machines, and the group of elementary Turing machines. The authors demonstrate that while the groups of oblivious and elementary Turing machines are finitely generated, the groups of finite-state automata and reversible Turing machines are not. Additionally, the article discusses the undecidability of the torsion problem for certain groups, including the group of elementary Turing machines, and establishes connections to cellular automata and topological dynamics. The findings contribute to the understanding of the computational properties and limitations of these abstract machines. [Extracted from the article]
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  Data: The group of reversible turing machines: subgroups, generators, and computability – CORRIGENDUM.
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  Data: Forum of Mathematics, Sigma; 2025, Vol. 13, p1-42, 42p
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  Data: <searchLink fieldCode="DE" term="%22Turing+machines%22">Turing machines</searchLink><br /><searchLink fieldCode="DE" term="%22Reversible+computing%22">Reversible computing</searchLink><br /><searchLink fieldCode="DE" term="%22Program+generators+%28Computer+programs%29%22">Program generators (Computer programs)</searchLink><br /><searchLink fieldCode="DE" term="%22Subgroup+analysis+%28Experimental+design%29%22">Subgroup analysis (Experimental design)</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+state+machines%22">Finite state machines</searchLink><br /><searchLink fieldCode="DE" term="%22Recursion+theory%22">Recursion theory</searchLink>
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  Label: Abstract
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  Data: The article focuses on the study of an abstract group of reversible Turing machines, exploring their subgroups, generators, and computability aspects. It identifies three significant subgroups: the group of finite-state automata, the group of oblivious Turing machines, and the group of elementary Turing machines. The authors demonstrate that while the groups of oblivious and elementary Turing machines are finitely generated, the groups of finite-state automata and reversible Turing machines are not. Additionally, the article discusses the undecidability of the torsion problem for certain groups, including the group of elementary Turing machines, and establishes connections to cellular automata and topological dynamics. The findings contribute to the understanding of the computational properties and limitations of these abstract machines. [Extracted from the article]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Forum of Mathematics, Sigma is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1017/fms.2025.10142
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      – Code: eng
        Text: English
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        PageCount: 42
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    Subjects:
      – SubjectFull: Turing machines
        Type: general
      – SubjectFull: Reversible computing
        Type: general
      – SubjectFull: Program generators (Computer programs)
        Type: general
      – SubjectFull: Subgroup analysis (Experimental design)
        Type: general
      – SubjectFull: Finite state machines
        Type: general
      – SubjectFull: Recursion theory
        Type: general
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      – TitleFull: The group of reversible turing machines: subgroups, generators, and computability – CORRIGENDUM.
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              Text: 2025
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              Y: 2025
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