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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Categorically exhaustive reasoning applied to the decision to
 abort
Date: Wed, 27 Mar 2024 10:55:25 +0100
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Op 26.mrt.2024 om 15:43 schreef olcott:
> On 3/26/2024 3:51 AM, Fred. Zwarts wrote:
>> Op 25.mrt.2024 om 23:50 schreef olcott:
>>> On 3/24/2024 11:42 AM, Mikko wrote:
>>>> On 2024-03-24 03:39:12 +0000, olcott said:
>>>>
>>>>> On 3/23/2024 9:54 PM, immibis wrote:
>>>>>> On 24/03/24 03:40, olcott wrote:
>>>>>>> On 3/23/2024 9:34 PM, immibis wrote:
>>>>>>>> On 24/03/24 03:15, olcott wrote:
>>>>>>>>> On 3/23/2024 8:40 PM, immibis wrote:
>>>>>>>>>> On 24/03/24 00:29, olcott wrote:
>>>>>>>>>>> On 3/23/2024 5:58 PM, immibis wrote:
>>>>>>>>>>>> On 23/03/24 16:02, olcott wrote:
>>>>>>>>>>>>> (b) H(D,D) that DOES abort its simulation is correct
>>>>>>>>>>>>>      (ABOUT THIS ABORT DECISION)
>>>>>>>>>>>>>      because it would halt and all deciders must always halt.
>>>>>>>>>>>>
>>>>>>>>>>>> To be a decider it has to give an answer.
>>>>>>>>>>>>
>>>>>>>>>>>> To be a halt decider it has to give an answer that is the 
>>>>>>>>>>>> same as whether the direct execution of its input would halt.
>>>>>>>>>>>
>>>>>>>>>>> That would entail that
>>>>>>>>>>
>>>>>>>>>> Tough shit. That is the requirement.
>>>>>>>>>
>>>>>>>>> I proved otherwise in the parts you erased.
>>>>>>>>
>>>>>>>> You proved that the requirement is not actually the requirement?
>>>>>>>
>>>>>>> I proved that it cannot be a coherent requirement, it can still
>>>>>>> be an incoherent requirement. Try and think it through for yourself.
>>>>>>
>>>>>> Every program/input pair either halts some time, or never halts.
>>>>>> Determining this is a coherent requirement.
>>>>>
>>>>> That part is coherent.
>>>>
>>>> The part that this determination must be done by a Turing machine
>>>> using descriptions of the program and input is coherent, too.
>>>>
>>>
>>> Every decider is required by definition to only report on what
>>> this input specifies.
>>>
>>> int sum(int x, int y){ return x + y; }
>>> sum(3,4) is not allowed to report on the sum of 5 + 6
>>> even if you really really believe that it should.
>>>
>>
>> Exactly! Therefore H(D,D), where D is based on H that aborts and 
>> returns false, so that D halts, should not return a report about 
>> another D that does not halt, even if you really really believe that 
>> it should.
> 
> There is enough information for sum(3,4) to compute the sum of 3+4.
> There is NOT enough information for sum(3,4) to compute the sum of 5+6.
> 
> There is enough information for H1(D,D) to compute Halts(D,D).
> There is NOT enough information for H(D,D) to compute Halts(D,D).
> 

But it is possible to create a simulating sum decider that aborts sum 
and returns the sum of 5+6 and then claim that it is right, because it 
has not enough information to calculate 3+4. It is possible, but wrong.
The only reason it has not enough information, is that it aborts 
prematurely. That makes the decision to abort wrong. This holds for H as 
well.