On Thu, 1 Jan 2004 00:15:20 +0000 (UTC), A.Sloman@cs.bham.ac.uk wrote:
>However, if deciding how an arbitrary program should be optimised is as
>difficult as deciding whether an arbitrary procedure will ever halt,
It is.
>then we have problems.
Happy New Year ;-).
But it depends on what you mean by "optimised" -- would optimising
the depth first search in TEACH TOWER into a polynomial time
algorithm, if it is possible[1], count as an "optimisation"?
How about optimising a bubble sort into, say, quicksort[2] or
one of the better sorts?
[1] It's attempting to solve the knapsack problem, which is one
of the familiar NP-complete problems, so we don't *know* if it
is possible, although it is strongly believed that it isn't.
[2] Which has bad "worst case" behaviour, so your optimiser
would have to know something about the likely distribution of
data to be sorted: it could, in some case, be *worse* than
bubblesort, IIRC. Therefore, your optimiser needs to be
psychic, and psychic computers have yet to be developed ...
so it's actually a *harder* problem than the halting problem.
Jonathan
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