Ben Goertzel <[EMAIL PROTECTED]> wrote: On Wed, Feb 20, 2008 at 4:27 PM, J
Storrs Hall, PhD wrote:
> OK, imagine a lifetime's experience is a billion symbol-occurences. Imagine
> you have a heuristic that takes the problem down from NP-complete (which it
> almost certainly is) to a linear system, so there is an N^3 algorithm for
> solving it. We're talking order 1e27 ops.
That's kind of specious, since modern SAT and SMT solvers can solve many
realistic instances of NP-complete problems for large n, surprisingly quickly...
and without linearizing anything...
Worst-case complexity doesn't mean much...
ben
I think you may both be off the track here. Although many difficult problems
for large n can be solved with contemporary solvers (and approximations to
those that cannot be can be used in their stead) many of the kinds of problems
that need to be solved cannot be approximated.
I don't think that J Storrs Hall example of a lifetime's experience (a billion
symbols) is truly relevant. No one actually believes that the human mind is
capable of analyzing reality into a monotonic (pure hierarchal) logic and there
is not much reason to believe that an effective AGI would have to be. But
there is a lot of reason to believe that increasing the capacity of logic
solvers dramatically would be useful.
To get back to Ben's statement: Is the computer chip industry happy with
contemporary SAT solvers or would a general solver that is capable of beating
n^4 time be of some use to them? If it would be useful, then there is a reason
to believe that it might be useful to AGI.
Jim Bromer
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