Timeline for Derivable relations in a monoid
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2021 at 17:36 | history | edited | diddy | CC BY-SA 4.0 |
added 8 characters in body
|
| Mar 13, 2021 at 17:25 | comment | added | Benjamin Steinberg | @Carl-FredrikNybergBrodda, yes. That is why is miswrote the rule in the comment a moment ago. | |
| Mar 13, 2021 at 17:25 | history | edited | diddy | CC BY-SA 4.0 |
added 5 characters in body
|
| Mar 13, 2021 at 17:24 | comment | added | Carl-Fredrik Nyberg Brodda | Ah, I see now that he defines his rewriting system mirrored to his original presentation. That's what I was missing. | |
| Mar 13, 2021 at 17:23 | comment | added | Benjamin Steinberg | @Carl-FredrikNybergBrodda Two $\hat{x_i}x_j$ with possibly j=I overlap | |
| Mar 13, 2021 at 17:22 | comment | added | Benjamin Steinberg | @Carl-FredrikNybergBrodda sorry I miswrote. He only moves hats right. So there is no rule x1 hat x2 | |
| Mar 13, 2021 at 17:20 | comment | added | Carl-Fredrik Nyberg Brodda | @BenjaminSteinberg The word $x_1 \hat{x}_2 x_2$ is an overlap (an extra hat got added in a couple of places in my original comment), no? It can be rewritten to two different words $\hat{x}_2 x_1 x_2$ and $x_1$. | |
| Mar 13, 2021 at 17:15 | comment | added | Benjamin Steinberg | This is a pretty simple complete rewriting system and so Newman does all the work | |
| Mar 13, 2021 at 17:15 | comment | added | Benjamin Steinberg | @Carl-FredrikNybergBrodda all is rules move hats to the left so there is never an ambiguity. You can only apply rules disjointly | |
| Mar 13, 2021 at 17:13 | comment | added | Benjamin Steinberg | @Carl-FredrikNybergBrodda what you wrote is not an overlap. His rule is to move hats to the left. I think the proof he wrote is fine | |
| Mar 13, 2021 at 17:01 | history | edited | diddy | CC BY-SA 4.0 |
edited body
|
| Mar 13, 2021 at 17:01 | comment | added | Carl-Fredrik Nyberg Brodda | You are missing many cases of local confluence (and this is the only non-trivial part of this being a complete rewriting system, so it is very important to get right!). For example, if you have $x_1 \hat{x}_2 \to \hat{x}_2 x_1$ and $\hat{x}_2 \hat{x}_2 \to 1$, then these overlap in the word $w \equiv x_1 \hat{x}_2 \hat{x}_2$. | |
| Mar 13, 2021 at 16:56 | history | edited | diddy | CC BY-SA 4.0 |
edited body
|
| Mar 13, 2021 at 16:54 | comment | added | diddy | @LSpice you are right. Thanks. I change that. | |
| Mar 13, 2021 at 16:52 | comment | added | LSpice | Do you really mean "words of the form $w = u v w$"? I understand that there's no contradiction since you're working in a monoid rather than a group, but it looks a little surprising. | |
| Mar 13, 2021 at 16:51 | history | edited | LSpice | CC BY-SA 4.0 |
Link to @BenjaminSteinberg's comment
|
| Mar 13, 2021 at 16:48 | history | edited | diddy | CC BY-SA 4.0 |
added 19 characters in body
|
| Mar 13, 2021 at 16:40 | history | answered | diddy | CC BY-SA 4.0 |