Acknowledgements

I am grateful to A. Aho, C. Bennett, J. Conway, D. Hillis, L. Hurd, D. Lind, O. Martin, M. Mendes France, J. Milnor, A. Odlyzko, N. Packard, J. Reeds, and many others for discussions. A preliminary version of this paper was presented at a workshop on ``Coding and Isomorphisms in Ergodic Theory,'' held at the Mathematical Sciences Research Institute, Berkeley (December 8--13, 1983). I thank M. Boyle, E. Coven, J. Franks, and many of the other participants for their comments. Some of the results given above were obtained using the computer mathematics system SMP [50].

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