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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory
Subject: Re: Categorically exhaustive reasoning applied to the decision to
 abort
Date: Wed, 27 Mar 2024 09:04:17 -0500
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On 3/27/2024 4:32 AM, Mikko wrote:
> On 2024-03-26 14:41:08 +0000, olcott said:
> 
>> On 3/26/2024 3:50 AM, Mikko wrote:
>>> On 2024-03-25 22:52:18 +0000, olcott said:
>>>
>>>> On 3/24/2024 9:27 AM, Mikko wrote:
>>>>> On 2024-03-24 02:11:34 +0000, olcott said:
>>>>>
>>>>>> On 3/23/2024 7:31 PM, Richard Damon wrote:
>>>>>>> On 3/23/24 7:29 PM, 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 H must report on different behavior
>>>>>>>> than the behavior that H actually sees thus violate the
>>>>>>>> definition of a decider that must compute the mapping from
>>>>>>>> its inputs...
>>>>>>>
>>>>>>> Nope.
>>>>>>> You are just showing yourself to be a stupid liar.
>>>>>>>
>>>>>>> Where in the DEFINITION of Compute the Mapping of the Input to 
>>>>>>> the Mapped Output does it say that the decider has to be able to 
>>>>>>> "see" that property of the input?
>>>>>>>
>>>>>>
>>>>>> In order to compute the mapping from an input there must be
>>>>>> some basis that is directly provided by this input.
>>>>>
>>>>> If no such basis is in the input the problem has no soution.
>>>>>
>>>>
>>>> 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.
>>>
>>> Your and my beliefs don't matter. Testers call the function with
>>> various pairs of inputs and compare the result to the specification.
>>> If the result is not what the specification requires then the function
>>> is wrong and needs be fixed or rejected.
>>>
>>
>> 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).
> 
> There is enough information to determine whether the result is as
> required by the specification.
> 

This specification only requires a mapping from H(D,D)
to Halts(Simulated_by_H(D,D)) and it gets that one correctly.
D(D) does not halt from the POV of H.

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