Snakes and cellular automata: Reductions and inseparability results

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. © 2011 Springer-Verlag Berlin Heidelberg.