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digitalmars.D.announce - Re: NP=P

Andrei Alexandrescu Wrote:

 Tim M wrote:
 If they really did find proof that p==np wouldn't they be millionaires 
 and probably should have kept it to themselves. (I haven't read that all 
 the way through btw)
 On Sun, 14 Dec 2008 08:43:48 +1300, BCS <ao pathlink.com> wrote:
 Reply to Knud,

 Lęs lige denne artikel

If I'm reading that correctly, not exactly, the verbiage seems to imply that they didn't solve P=NP but a related problem. "... these problems most of which are not believed to have even a polynomial time sequential algorithm."

The paper shows that #P=FP. I'm not that versed with theory to figure how important that result is. http://en.wikipedia.org/wiki/Sharp-P http://en.wikipedia.org/wiki/FP_(complexity) Andrei

Proving FP=#P is a far more grandiose claim than proving P = NP. To clarify: FP is the class of all *functions* that can be computed 'easily' (on a deterministic computer in polynomial time). It is a pretty simple generalization of, P, which is the class of easy *decision problems* (must have a yes/no answer.) While on the other hand: #P is the set of all functions which compute the number of solutions for problems in NP. For example, *counting* the number of Hamiltonian circuits in a graph is in #P, while simply *testing* if it has Hamiltonian circuit is in NP. If this were indeed true, it would have many screwy consequences, such as NP=coNP (but then again pretty much any hierarchy collapse would do the same thing.) Of course, most likely this is just noise.
Dec 22 2008