> > I'm sorry but I still don't understand exactly what you mean by "Is
> computer
> > program-instance X a TM with respect to problem P"
>
> Each TM (or algorithm) is defined with respect to a "problem",
> which is set
> of valid input strings. Each string in the set is a problem instance, ans
> the system's output at a final state is the solution to that problem
> instance. When we discuss whether a system can be seen as a TM, it is
> always respect to a problem in this sense.
OK, but that is not the only reasonable formulation of "problem"
Let's try another one...
What if we define the problem instead as a "fitness function", and say that
different TM outputs can have different "degrees of quality" as problem
solutions, where the degree of quality is in [0,1].
Then we can assess the degree to which a TM is able to solve a problem, as
an average over all problem instances
> > To get more concrete, suppose we carry out the following experiment:
> >
> > "Take a specific NARS instance in a particular state. Call it
> X. Give it
> a
> > query in a specific format, which asks it to sort a list of n numbers.
> > Then, calculate the amount of time X takes before it delivers a correct
> > answer to the question (a correct sorting of the list) in a specified
> > format."
>
> This is a bad example --- you are asking NARS to simulate a TM.
> In doing so,
> of course it behaves like one.
>
> When I say NARS is not a TM, I'm not saying that it cannot
> simulate a TM in
> certain situations (and you know this for sure). The interesting situation
> is when it doesn't silutate a TM. Soring is a problem for it "correct
> answer" is well-defined, and the system can have sufficient knowledge and
> resources to solve it.
OK, so what if the problem is "create a poem that x% of humans will find
beautiful."
Then there is no one correct answer, but different outputs ("answers") will
have different degrees of quality.
And we can, by running multiple replicants of the same NARS instance with
the same initial state, assess the amount of time it will take the NARS
instance (worst case & average case .. though I guess the worst case will be
infinity) to solve the problem for each value of x.
On the other hand if we make the task less vague, and have just "create a
poem that humans will find beautiful", then we do not have a precisely
defined problem, and computation theory is not very useful, as it applies
only to precisely defined things.
[If you're going to say that the performance of a system according to
imprecisely given criteria, can't be modeled using computation theory, for
sure no one is going to argue with you !! ]
-- Ben
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