Timeline for Probabilistic 2D cellular automata with memory lifetime increasing like $e^{L^2}$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 21 at 16:19 | comment | added | Andi Bauer | So the idea is that while the noise is what we're protecting against, it also helps protecting from either flipping a single row to get into a stable not-all-0-and-not-all-1 state, or (per your answer) flipping a cross to flip from all-0 to all-1. I'm aware that for the noise model that Toom and Gacs use in their proofs, noise can never "help you" in that way. What I'm considering here is noise defined as a uniform perturbation of the probabilistic CA rules. You can also use a "perturbed" probabilistic Tooms rule to start with, then it should be robust to the usual noise model. | |
| May 21 at 16:10 | comment | added | Andi Bauer | Thanks, that's an intriguing thought! I'm not entirely convinced yet: If we flip $O(L)$ sites to create a "thin cross" on the torus, then it'll take $O(L)$ time for the CA to widen the row and column forming this cross. During this time, the noise will have very likely broken up the cross. A single row/column is very unstable to noise, as soon as one site flips, the CA will start erasing that row/column. | |
| May 21 at 12:27 | history | answered | Ilmari Karonen | CC BY-SA 4.0 |