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Some undecidable problems about the trace-subshift associated to a Turing machine

Abstract : We consider three problems related to dynamics of one-tape Turing machines: Existence of blocking configurations, surjectivity in the trace, and entropy positiveness. In order to address them, a reversible two-counter machine is simulated by a reversible Turing machine on the right side of its tape. By completing the machine in different ways, we prove that none of the former problems is decidable. In particular, the problems about blocking configurations and entropy are shown to be undecidable for the class of reversible Turing machines.
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Anahí Gajardo, Nicolas Ollinger, Rodrigo Torres-Avilés. Some undecidable problems about the trace-subshift associated to a Turing machine. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.267-284. ⟨10.46298/dmtcs.2137⟩. ⟨hal-01349052⟩

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