## 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:

Lęs lige denne artikel
http://arxiv.org/abs/0812.1385

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

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