Re: What is the Result from Invoking this Halt Function?
From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/14/04
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Date: Sat, 14 Aug 2004 16:33:20 GMT
"Will Twentyman" <wtwentyman@read.my.sig> wrote in message news:411a779e$1_4@newsfeed.slurp.net...
> Peter Olcott wrote:
>
> > "Will Twentyman" <wtwentyman@read.my.sig> wrote in message news:4118e82c$1_5@newsfeed.slurp.net...
> Here is where your analysis begins to fail. First, HALT may or may not
> be running on a UTM. If it is not running on a UTM, it cannot query the
> UTM.
I am only required to provide a single case where my method is not
prohibited from working. I assume as an integral part of this single
case a UTM.
> Second, HALT does its processing bases only on its input. Context
> is meaningless because there is only one context, the machine itself.
This is merely a False and Unsupported Assumption (FUA).
This a purely arbitrary restriction that has nothing at all to do with providing
the design for a machine that can correctly determine whether or not each
and every element of the universal set of Turing Machines halts on a specific
input.
> If it is being emulated on a UTM, that fact cannot affect its results or
> you are not emulating HALT.
I am not emulating your pure arbitrary (and thus meaningless) restriction.
Emulating arbitrary restrictions is not required.
> HALT does not have three possible outputs.
> It has two possible outputs <TM(input) halts> and <TM(input) does not
> halt>. The method of encoding those outputs is irrelevant.
That is the way that it now works. There is no longer a third output.
I will update my website to provide this update.
> If you make the modifications that you propose, several things result:
> First, you are no longer discussing the Halting Problem.
We are discussing any and all proof that a TM that can determine
whether or not any TM halts on a specific input is impossible.
Every single published source that I have encountered calls this
the Halting Problem, including Turing himself.
Halting Problem according to Alan Turing:
The problem of finding out whether a given number is the D.N of a
circle-free machine, and we have no general process for doing this
in a finite number of steps. In fact, by applying the diagonal process
argument correctly, we can show that there cannot be any such general
solution.
> Second, you are no longer discussing UTMs.
I augmented the basic definition of a UTM slightly. This is not anywhere
near an impossible task. For anyone that knows finite automatons, this
is trivial.
> Third, any conclusions you draw from the new situation are unrelated to
> the Halting Problem.
I have completely refuted each point that you made, point-by-point.
I have already completely refuted this latter point in my refutations above.
I have refuted the proof that solving the Halting Problem is impossible
according to Alan Turing's own definition of the Halting Problem.
> You have talked about the fact that you are a programmer. Surely, as a
> programmer, you are aware of the fact that when you are asked to
> construct something, it must behave in a specified way. For example, a
> stack must provide the functionality push() and pop() at the very least.
> If you are told what push() and pop() are supposed to do as your part
> of a larger program, you cannot *change* that behavior to suit your
> purposes. If you do, the work others will be doing will be incorrect.
> The bug lies in your change, not in their work. The same is true here.
> You cannot change the behavior of things and claim they have anything
> to do with what is originally specified.
>
> --
> Will Twentyman
> email: wtwentyman at copper dot net
>
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