20 Nov
2003
20 Nov
'03
5:55 p.m.
From:
ard(a)p850ug1.demon.co.uk
>
> In the case of Turing closure, the notion is much broader.
Turing closure
> refers
> to the ability of a system to perform any and all computations
that can be
> expressed. Now, there are problems with this
notion, since
Godel has shown
> that some expressible computations in fact
can not be
computed. Still, the
> general notion is: all that can be computed
is computable upon
a TM, and a
TM
is capable of computing all computations.
Care to explain this in a way which is not either self-contradictory
('There are functions that can't be computed, but a Turing machine can
computer all functions) or tautological ('A Turing machine can compute
all functions that can be computed on a Turing machine')?
-tony