Wikipedia:Reference desk/Archives/Mathematics/2013 May 26
| Mathematics desk | ||
|---|---|---|
| < May 25 | << Apr | May | Jun >> | May 27 > |
| Welcome to the Wikipedia Mathematics Reference Desk Archives |
|---|
| The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
May 26
[edit]P!=NP based on its own proof difficulty?
[edit]Scott Aaronson has said that P versus NP is itself in NP and would probably be easy to prove if P=NP. Our article P versus NP problem#Results about difficulty of proof indicates that several methods of proof have been shown not to be possible. This suggests that if that list were expanded, a proof of the following form might be possible: "If P=NP, then the proof that P=NP is NP-easy; therefore, it can be proven using one of these methods; but previous theorems show it can't be decided using any of those methods, therefore P!=NP." Has this approach been investigated? NeonMerlin 19:54, 26 May 2013 (UTC)
- I'm skeptical that this approach can be made to work (there are a lot of obvious gaps, as I'm sure you've noticed yourself — that doesn't mean they can't be closed, but I'm skeptical).
But really this isn't the right place to discuss it. Maybe ask at WP:RD/Math and see if anyone can provide more insight? --Trovatore (talk)20:31, 26 May 2013 (UTC) Oops, sorry, this was dumb — this is the refdesk. Sorry about that. I thought this was the P=NP page. --Trovatore (talk) 20:53, 26 May 2013 (UTC)
I am about to write a Bachlor thesis on Green's relations for semigroups.
Unfortunately, Wikipedia and my books only tell me that they are important, but not why. Can somebody help me? I can not see why Green's relations are so useful (like it is stated in the Wikipedia article in the introduction). Don't get me wrong: I do not need any applications "in the real world", but I would like to know why they are so useful. Could someone give me "simple consequences"? And, since my books only tell me something like "If the semigroup has a certain form, then Green's relations do this and this" (and not the other way round): How can Green's relations tell me something about the semigroup, if I need to know the semigroup's properties before? — Preceding unsigned comment added by 83.64.56.34 (talk) 22:00, 26 May 2013 (UTC)