On Fri, 4 Jan 2002, Tomasz Wegrzanowski wrote:

> Let P be the problem space, that is set of all problems that can be
> solved by any language. Requirements like speed are part of promlem.
> Let difficulty of solving a problem be defined with positive real
> number. No let's f_L(p) be function that gives difficulty of solving
> problem p \in P in language L. This function changes to some extend
> from one programmer to another. Now let's D(p)->R_{0+}, p \in P be
> interest density function, that is, function that shows what problems
> you are most interested in.

I think you're better off defining a measure... well I don't know, but I
wouldn't think of a problem space as continuous enough to warrant defining
a density. The question would be "what is your total interest in this set
of problems", that is, a power(Problems) -> R_{0+} function, such that it
is homomorphic under addition (set addition is union presuming mutually
exclusive sets), and M(x)+M(not x) = M(everything)...

> Our task is to find L that minimizes expresion \int D(p)*f_L(p) dp

I think there are infinitely many "interesting" (non-zero interest)
solvable problems that are arbitrarily difficult to solve in whatever
language... which would mean that this integral diverges... which is not a
good think if you're trying to optimise its value. Ok, I don't have much
to back my claims, and I'm can't convince myself terribly.

________________________________________________________________
Mathieu Bouchard                   http://hostname.2y.net/~matju