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Dec 10 at 4:05 answer added Ville Salo timeline score: 5
Dec 9 at 22:33 history became hot network question
Dec 9 at 16:27 vote accept Dominic van der Zypen
Dec 9 at 15:47 answer added Martin M. W. timeline score: 12
Dec 9 at 15:26 comment added Dominic van der Zypen Thanks @VilleSalo, an answer would be very much appreciated!
Dec 9 at 15:07 comment added Ville Salo AND is not surjective, so not 2-to-1. I can write an answer at some point. A key point for doing one-sided is that xor is left-permutive, I guess that's what I meant when I said it's one-sided.
Dec 9 at 14:51 comment added Dominic van der Zypen Is ${\tt AND}$ , $\land$, a two-to-one cellular automaton? If yes, the argument would not work. If we take $s = {\tt 01\, 001\, 0001 \, 00001}\ldots$ then $s \land \ell_1(s)$ is the constant 0 sequence. A similar argument can be made for ${\tt OR}$, $\vee$. Maybe you can elaborate your argument in an answer - many thanks.
Dec 9 at 14:47 comment added Ville Salo (This argument is clearer for two-sided sequences, but the CA is one-sided so it works out)
Dec 9 at 14:40 comment added Ville Salo No, xor is a two-to-one cellular automaton. A periodic point generates a finite subshift under the shift, so the preimage subshift is finite, so has only periodic points.
Dec 9 at 14:31 history asked Dominic van der Zypen CC BY-SA 4.0