Abstract
A careful analysis of an old undecidability proof reveals that periodicity and non-surjectivity of two-dimensional cellular automata are recursively inseparable properties. Analogously, Wang tile sets that admit tilings of arbitrarily long loops (and hence also infinite snakes) are recursively inseparable from the tile sets that admit no loops and no infinite snakes. The latter inseparability result actually implies the first one in a trivial way.
Research supported by the Academy of Finland Grant 131558.
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Kari, J. (2011). Snakes and Cellular Automata: Reductions and Inseparability Results. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_17
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