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Journal Articles Journal of Computer and System Sciences Year : 2017

A Small Minimal Aperiodic Reversible Turing Machine

Abstract

A simple reversible Turing machine with four states, three symbols and no halting configuration is constructed that has no periodic orbit, simplifying a construction by Blondel, Cassaigne and Nichitiu and positively answering a conjecture by Kari and Ollinger. The constructed machine has other interesting properties: it is symmetric both for space and time and has a topologically minimal associated dynamical system whose column shift is associated to a substitution. Using a particular embedding technique of an arbitrary reversible Turing machine into the one presented, it is proven that the problem of determining if a given reversible Turing machine without halting state has a periodic orbit is undecidable.

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Other [cs.OH]
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Dates and versions

hal-00975244 , version 1 (08-04-2014)

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Cite

Julien Cassaigne, Nicolas Ollinger, Rodrigo Torres. A Small Minimal Aperiodic Reversible Turing Machine. Journal of Computer and System Sciences, 2017, 84, pp.288-301. ⟨10.1016/j.jcss.2016.10.004⟩. ⟨hal-00975244⟩
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