From: fudley (fuddley@fastmail.fm)
Date: Sat May 22 2004 - 09:31:43 MDT
On Fri, 21 May 2004 "J. Andrew Rogers" <andrew@ceruleansystems.com> said:
>all real computers are – Finite Turing Machines. UTMs are a
>mathematical amusement, and not relevant
As a practical matter your distinction doesn’t seem very important. An
infinite UTM will keep going chasing its own tail forever; A real finite
machine will keep going until all the memory space is used up and then it
will freeze. Either way its bad news.
And don’t forget my original point, the more unchangeable hardwired
axioms that say, “regardless of circumstances whenever you encounter
situation X you must perform action Y, absolutely positively no
exceptions”, the more unreliable the system will become because sometimes
action Y is imposable.
> On a finite machine, it is quite possible to show that some specific
> implementation will always halt.
It’s no different in a infinite machine, some specific programs will
always halt, some will never halt, and some you just don’t know. It would
be nice if you could at least identify things that were either false or
true but un-provable so we could stop wasting time over them, but Turing
proved even that could not be done.
John K Clark
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