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

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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