Wikipedia:Reference desk/Archives/Mathematics/2013 May 26

= May 26 =

P!=NP based on its own proof difficulty?
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 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? Neon Merlin  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 &mdash; 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 &mdash; this is the refdesk.  Sorry about that.  I thought this was the P=NP page. --Trovatore (talk) 20:53, 26 May 2013 (UTC)

Green's relations
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)