Hello Ivan,
If P = NP it would mean that, given a problem reframed as reasoning
such that its solution is a proof p of size s, one could construct p
in a polynomial time of s, which sounds very doubtful.
That's in theory, in practice however I think we could make P = NP for
some class of inputs via clever use of meta-learning (such as
inference control meta-learning that we're experimenting within
opencog, see
https://blog.singularitynet.io/introspective-reasoning-within-the-opencog-framework-1bc7e182827).
In fact I had this dream where we could have a sequence of NP problems
and progressively learn how to solve them in P.
Obviously for a finite set of inputs, one can turn any complex
algorithm into a logarithmic one (think of a pre-calculated binary
decision tree, where each branch is a bit describing the input and
each leaf is the solution). But it should still be possible to learn
an actual algorithm rather than a finite giant decision tree, that
performs worse that log, is more compact, but performs better than NP
for a bunch of real-world problems.
Nil
On 11/6/18 7:00 PM, Ivan Vodišek wrote:
Hello everyone :)
I have a question regarding to my independent research relating to
OpenCog. I read somewhere (I really don't remember where) that if P = NP
<https://en.wikipedia.org/wiki/P_versus_NP_problem> then it would be
beneficial to AI in general.
There are science fields which would obviously benefit if P = NP. But my
question is: how would specifically OpenCog benefit from that solution?
Somehow, it should be a matter of reducing a large number of possible
combinations, but I don't really see were would AI fit into this
equation. Googling around didn't produce anything interesting, so I'm
making a post to this OpenCog community in a hope for an answer.
Thank you all for your time,
Ivan V.
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