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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Categorically exhaustive reasoning applied to the decision to abort
Date: Tue, 2 Apr 2024 11:00:23 +0300
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On 2024-04-01 14:52:57 +0000, olcott said:

> On 4/1/2024 3:15 AM, Mikko wrote:
>> On 2024-03-31 16:29:06 +0000, olcott said:
>> 
>>> On 3/31/2024 11:17 AM, olcott wrote:
>>>> On 3/31/2024 11:08 AM, Mikko wrote:
>>>>> On 2024-03-31 14:25:37 +0000, olcott said:
>>>>> 
>>>>>> On 3/31/2024 4:04 AM, Mikko wrote:
>>>>>>> On 2024-03-30 13:45:03 +0000, olcott said:
>>>>>>> 
>>>>>>>> On 3/30/2024 2:09 AM, Mikko wrote:
>>>>>>>>> On 2024-03-29 14:26:50 +0000, olcott said:
>>>>>>>>> 
>>>>>>>>>> On 3/29/2024 6:10 AM, Mikko wrote:
>>>>>>>>>>> On 2024-03-28 15:38:08 +0000, olcott said:
>>>>>>>>>>> 
>>>>>>>>>>>> On 3/28/2024 9:44 AM, Mikko wrote:
>>>>>>>>>>>>> On 2024-03-27 14:04:17 +0000, olcott said:
>>>>>>>>>>>>> 
>>>>>>>>>>>>>> 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.
>>>>>>>>>>>>> 
>>>>>>>>>>>>> What "this pecification"? This means the one you refer or point to
>>>>>>>>>>>>> but you didn't.
>>>>>>>>>>>>> 
>>>>>>>>>>>> 
>>>>>>>>>>>> Every implementation of H(D,D) that simulates its input must abort
>>>>>>>>>>>> this simulation or never itself halt.
>>>>>>>>>>>> 
>>>>>>>>>>>> int main() { D(D); }   is not a D simulated by H.
>>>>>>>>>>>> int main() { H(D,D); } is a D simulated by H.
>>>>>>>>>>> 
>>>>>>>>>>> Does not answer what "this specification" means above.
>>>>>>>>>>> 
>>>>>>>>>> 
>>>>>>>>>> *THIS SPECIFICATION*
>>>>>>>>>> Every implementation of H(D,D) that simulates its input must abort
>>>>>>>>>> this simulation or never itself halt.
>>>>>>>>> 
>>>>>>>>> Are you sure you want to allow that H(D,D) may run un a loop and never
>>>>>>>>> halt and never continue the simulation?
>>>>>>>>> 
>>>>>>>> 
>>>>>>>> So you didn't understand the: *must abort this simulation* part ?
>>>>>>> 
>>>>>>> I did. I asked whether whether you really mean all that "never iself
>>>>>>> halt" means.
>>>>>>> 
>>>>>> 
>>>>>> 01 void D(ptr x) // ptr is pointer to void function
>>>>>> 02 {
>>>>>> 03   H(x, x);
>>>>>> 04   return;
>>>>>> 05 }
>>>>>> 06
>>>>>> 07 void main()
>>>>>> 08 {
>>>>>> 09   H(D,D);
>>>>>> 10 }
>>>>>> 
>>>>>> *Execution Trace*
>>>>>> Line 09: main() invokes H(D,D);
>>>>>> 
>>>>>> *keeps repeating* (unless aborted)
>>>>>> Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)
>>>>>> 
>>>>>> *Simulation invariant*
>>>>>> D correctly simulated by H cannot possibly reach past its own line 03.
>>>>>> 
>>>>>> As soon as line 03 would be simulated  H sees that D would call
>>>>>> itself with its same input, then H aborts D.
>>>>> 
>>>>> Looks like you don't know whether you really want to allow that H(D,D)
>>>>> may run in a loop and never halt and never continue the simulation.
>>>>> 
>>>> 
>>>> H(D,D) must halt or it cannot be any kind of decider. My other
>>>> reviewers consistently and perpetually lie about whether or
>>>> not H(D,D) is correct to abort its simulation.
>>>> 
>>> 
>>> When I refer to H I am referring to every element of the set of 
>>> implementations H that simulate their input.
>> 
>> I.e., every element of the set on implementations of oevery element
>> of the sent of implementataions of ....
>> 
> 
> Every element of the set of implementations of H(D,D) that simulates its
> input either aborts this simulation or is wrong.
> 
> It also must be the first directly executed element that performs
> the abort or none of them do because all of the H elements in a
> recursive simulation chain have the exact same machine code.

You seem to agree that "this pecification" is nomen nuduum.

-- 
Mikko