Timeline for Local rule for the product of two cellular automata
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2022 at 18:24 | answer | added | Ilmari Karonen | timeline score: 1 | |
| S Aug 19, 2022 at 17:10 | history | suggested | Ilmari Karonen | CC BY-SA 4.0 |
standardize and clarify notation, misc copyedits, generalize to allow different alphabets for original automata
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| Aug 19, 2022 at 15:19 | comment | added | Ilmari Karonen | (I'm a bit concerned that I may have misinterpreted your question, since it feels rather trivial after my edits, and in light of the fact that $A^{\mathbb Z} \times B^{\mathbb Z}$ is naturally isomorphic to $(A \times B)^{\mathbb Z}$. But this does seem to be the standard definition of product cellular automata as used e.g. in doi.org/10.1016/j.ic.2008.03.012 and arxiv.org/abs/0902.1441, just to name two of the results I found based on a quick Google search.) | |
| Aug 19, 2022 at 15:09 | comment | added | Ilmari Karonen | Hi, kiki, and welcome to MathOverflow. I've edited your question to (hopefully) standardize and clarify the notation a bit, and also to generalize it slightly to allow the original automata to have distinct alphabets $A$ and $B$. I hope I haven't introduced any errors while editing; if I have, please do correct them and feel free to improve or revert any changes I've made that you may disagree with. Thanks! | |
| Aug 19, 2022 at 15:06 | review | Suggested edits | |||
| S Aug 19, 2022 at 17:10 | |||||
| Aug 19, 2022 at 1:32 | comment | added | Joseph Van Name | The asterisk in the notation $A^Z*A^Z$ is not very clear to me. We would use the symbol $\times$ for the Cartesian product if we want to use the Cartesian product. And if we are using $Z$ to denote the integers, we would write $\mathbb{Z}$. | |
| Aug 18, 2022 at 23:39 | comment | added | Ville Salo | Increase neighborhoods artificially to be equal, take $B = A\times A$, use the obvious product of local rules. | |
| Aug 18, 2022 at 19:32 | history | edited | kiki | CC BY-SA 4.0 |
deleted 1 character in body; edited title
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| Aug 18, 2022 at 19:27 | comment | added | mathworker21 | @J.W.Tanner As the tag indicates | |
| Aug 18, 2022 at 19:24 | comment | added | J. W. Tanner | Plural of automaton is automata | |
| Aug 18, 2022 at 18:51 | history | asked | kiki | CC BY-SA 4.0 |