Re: What is the Result from Invoking this Halt Function?

From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 08/16/04 

Date: Mon, 16 Aug 2004 10:05:23 -0400

Peter Olcott wrote:

> "Will Twentyman" <wtwentyman@read.my.sig> wrote in message news:411e571e_3@newsfeed.slurp.net...
>
>>Peter Olcott wrote:
>>
>>
>>>"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.
>>
>>And you must also show that your case is not equivalent to a case where
>>it does not work. You have failed to do this.
>
> The burden of proof is on you. It totally obvious in any case.
> In one case a program such as LoopIfHalts can make the
> problem undecidable, and in the other case is it not undecidable.

How can it be on me when you have not completely defined your system
yet? You are claiming you have a different situation. I need to know
how your different situation works before I can analyze it. You have
more work to do.

> A program such as LoopIfHalts only loops iff halt returns true.
> Since halts simply halts whenever it is invoked as a part of
> any other TM's invocation, therefore halt never every returns
> anything at all like true to LoopIfHalts. Since halt already knows
> what Halts own behavior is in this case, it simply reports that
> LoopIfHalts halts.

But now LoopIfHalts doesn't know what to do. It's still waiting for a
result. What does LoopIfHalts do on no result? Secondly, can you claim
to have a halt analyzer when it doesn't analyze?

>>>>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).
>>
>>You would do well to drop these things. A TM is *defined* to operate
>>only on its input. It is assumed to be a machine. The fact that it can
>>be emulated on a UTM is coincidental.
>
> Then its invocation context is merely one additional input.
> You are not going to try to claim that a TM is defined to only
> have one input are you?

Again, there's the problem of definition: the halt analyzer doesn't care
about its context. It cares about what the code and input it receives
will do. Until you provide precise new definitions we can work with, we
will be nailing you with the only ones available to us.

>>>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.
>>
>>The assumed context is that it is not being called, but is a stand-alone
>>machine. The fact that it can be emulated is where the power of TMs arises.
>
> Unless you are prepared to prove that a UTM can not possibly look
> up a value in its own state transition matrix, then you must accept that
> the augmentation that I have specified is possible, and can be provided
> as input to the halt analyzer TM.

It can, but the halt TM cannot ask for it unless it is prepared to
discover it is not running on a UTM. At that point, the possibility of
the UTM it runs on lying to it must also be accounted for. If the Halt
Analyzer relies on something else giving it true information to produce
a true result, it's not a working halt analyzer.

>>>>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.
>>
>>Then you need to start clarifying what you are doing. Preferably on
>>your website with technical details of *how* things are being done. You
>>would also need to demonstrate how that work applies to the standard
>>situation.
>
> It's perfectly clear to me. The only way that I can make it more
> clear to others is by specific dialogue. They must point out what
> its not clear to them. If I was a professional writer, I probably could
> do better than this.

Definitions would be a good start. Since you are reading Turing's work,
you have plenty of examples of what definitions should look like.

>>>>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.
>>
>>It's not impossible, just a different system.
>
> Good we agree at least on one thing.
> It is not such a different system as to extend beyond the
> Church-Turing thesis. It is still a Turing Machine.

Maybe, maybe not. It's up to you to prove that it is equivalent to a
Turing Machine. You have not done that yet. There are theoretical
modifications that make Modified Turing Machines *not* computationally
equivalent to standard Turing Machines.

>>>>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 would do well to stop making such claims until you have a
>>significant number of people (more than 2) agreeing with you. Until
>>then, you come across as arrogant and/or ignorant.
>
> Truth exists independently of minds that know it.
> There could be a truth than no minds ever hold.
> Truth is not a democracy, each and every mind could disagree
> and every one of them could be wrong.
>
> You are asking for a little more humility?
> With the degree of abuse that I have taken here, I don't know
> if that would be a reasonable request. I will attempt this on a case
> by case basis.

Humility will take you far. I've been wrong in the past and David
Ullrich (among others) have called me on those mistakes. None of them
have heaped *any* abuse on me for it. 

-- 
Will Twentyman
email: wtwentyman at copper dot net

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