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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Hypothetical possibilities --- Complete Proof --- Halt State
Date: Sat, 3 Aug 2024 08:27:31 -0500
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On 8/2/2024 11:32 PM, Jeff Barnett wrote:
> On 8/2/2024 7:19 PM, Mike Terry wrote:
>> On 02/08/2024 23:42, Ben Bacarisse wrote:
>>> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
>>>
>>>> Of course these traces don't support PO's overall case he is claiming,
>>>> because the (various) logs show that DDD halts, and that HHH(DDD) 
>>>> reports
>>>> DDD as non-halting, exactly as Linz/Sipser argue. Er, that's about it!
>>>
>>> PO certainly used to claim that false (non-halting) is the correct
>>> result "even though DDD halts" (I've edited the quote to reflect a name
>>> change).  Unless he's changed this position, the traces do support his
>>> claim that what everyone else calls the wrong answer is actually the
>>> right one.
>>>
>>
>> So, in your opinion, what do you believe is PO's criterion for 
>> "correct result", exactly?  It would be handy if you can give a proper 
>> mathematical definition so nobody will have any doubt what it is. Hey, 
>> I know you're more than capable of getting a definition right, so 
>> let's have that definition!
>>
>> Definition:  A TM P given input I is said to "halt" iff ?????
>>               or whatever...
> 
> I think this is a rather hopeless venture without formally defining the 
> representation of a TM. For example: In some formulations, there are 
> specific states defined as "halting states" and the machine only halts 
> if either the start state is a halt state or there is a transition to a 
> halt state within the execution trace; 

void DDD()
{
   HHH(DDD);
   return;
}

This is the one that I am using.
The halt state is either the "return" instruction
of the the C function DDD or the "ret" instruction
of its assembly language translation.

> In another formulation, machines 
> halt if there is a transition to an undefined state. Note a few things: 
> 1) the if's above are really iff's, 2) these and many other definitions 
> all have equivalent computing prowess, 3) Some formulations define 
> results by what is left on the tape (or other storage device) while 
> others add the actual halting state to determine the results.
> 

This is the first excellent review related to my work
that I have ever seen from you.

> In a conversation about such topics, gentlemen of good faith and 
> reasonable knowledge can simple ignore these differences and not go off 
> the rails. This is not true when the pied piper is ignorant, 
> disillusional, and masturbating while simultaneously spinning a hula 
> hoop around his neck.
> 
>> It's easy enough to say "PO has his own criterion for halting, which 
>> is materially different from the HP condition, and so we all agree PO 
>> is correct by his own criterion, but that does not say anything about 
>> the HP theorem because it is different from the HP definition".
>>
>> But is that /really/ something PO agrees with?  I don't think so 
>> somehow, because I'm pretty sure PO believes his claim "refutes" the 
>> HP result.  He wouldn't say that if he freely acknowleded that he had 
>> invented a completely different definition for halting.  Also, for 
>> what you're saying to be the right way of looking at things, PO would 
>> have to admit that the HP proof with its standard definition of 
>> halting is valid, and that there is nothing wrong with the Linz proof, 
>> other than it not applying to his own favourite PO-halting definition.
>>
>> I.e. I think your way of looking at it is a bit "too easy" - but I'd 
>> be happy to be convinced! Personally I suspect PO has no such "new and 
>> different definition" and that anything along those lines PO is 
>> thinking of will be quite incoherent.  No doubt you could make some 
>> definition that is at least coherent but we have to ask ourselves - is 
>> that definition /really/ what PO is thinking???
>>
>> Nowadays, I think PO's position is more that:
>> -  yes, DDD() halts when run directly
>> -  but DDD() when it runs inside HHH simulator /really/ does not halt, 
>> in some kind of
>>     sense that it /really/ has infinite recursion which would never end
>>     however far it was simulated (because it "exhibits" infinite 
>> recursion in some way)
>> -  and yes, DDD() /does/ halt when simulated within UTM(DDD),
>> -  but the behaviour of DDD depends on who is simulating it.  It 
>> terminates when
>>     UTM simulates it, but doesn't terminate when HHH simulates it, due 
>> to some
>>     kind of pathelogical relationship specifically with HHH.  This 
>> difference in
>>     simulation is /more/ than one simulator aborting earlier than the 
>> other...-- 
> Jeff Barnett
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer