# Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable

@article{Jalonen2018ConjugacyOO, title={Conjugacy of One-Dimensional One-Sided Cellular Automata is Undecidable}, author={Joonatan Jalonen and Jarkko Kari}, journal={ArXiv}, year={2018}, volume={abs/1710.08111} }

Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively inseparable: (i) pairs where $F$ has strictly larger topological entropy than $G$, and (ii) pairs that are strongly conjugate and have zero topological entropy.
Because there is no factor map from a lower entropy system to a higher entropy one, and there is no…

## 6 Citations

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### Reversible Computation: Extending Horizons of Computing: Selected Results of the COST Action IC1405

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