Re: Can a regular Turing Machine provide Protected Memory?

From: Owen Jacobson (angstrom_at_lionsanctuary.net)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 07:31:19 GMT

On Sat, 28 Aug 2004 20:20:37 +0000, Peter Olcott wrote:

> If conditions were valid refutations then the correct conclusion that no
> computer can ever do anything would be derived. Since it is obvious that
> this is not a correct conclusion, therefore conditions can not form valid
> refutations.

Conditions don't form refutations, but they *do* limit the scope of any
proof they apply to. You are asserting that your Halts() functions
correctly within a UTM that correctly reports extra information beyond the
machine being analyzed and that machine's input. If you're correct, you
will have proven that a machine that provides that extra information can
analyze some programs some of the time -- but not when run on a UTM
that does not provide your information, which is still a TM that can
be validly constructed from your TM/UTM pair.

Until the condition is provably removed, any proof you offer is not
general to all possible situations, and as such does not form a
counterargument about the Halting problem, which has no such conditions.
It merely demonstrates what we already knew: that you can make a machine
that'll get the right answer about the Halting problem some, but not all,
the time. 

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