Re: Detecting infinite recursion (pathological self-reference error)

[olcott]

On 3/6/2021 9:12 AM, Richard Damon wrote:
> On 3/6/21 10:01 AM, olcott wrote:
>> On 3/6/2021 7:58 AM, Ben Bacarisse wrote:
>>> olcott <No...@NoWhere.com> writes:
>>>
>>>> You can understand that the reason that (at least) many decision
>>>> problems are undecidable is that both elements of the solution set:
>>>> true/false are contradicted.
>>>
>>> No.  Every single instance of any of the undecidable problems I listed
>>> has a correct yes/no answer.  Every context-free grammar either is or
>>> not ambiguous.  Every pair of TMs either compute the same function or
>>> they do not.  Every TM either writes an 'x' to its tape or it does not.
>>> These are simple and obvious problems that have no algorithmic solution.
>>>
>>> You need to stop doing linguistic gymnastics and start facing
>>> mathematical facts.
>>>
>>
>> Every single instance of any undecidable decision problem does not have
>> a solution that can be encoded because all of the answers that it can
>> provide are defined to be incorrect.
>
> The Halting status of H_Hat IS decidable once you have provided an H
> that meets the requirements of giving an answer in Finite time.
>>
>> Every decision problem has its entire solution set defined to be a
>> Boolean value of {true, false}.
>
> Yes, The Halting status of any true computation is True of False.
>>
>> If Halts((u32)H_Hat, (u32)H_Hat) returns true to H_Hat() meaning that
>> its input halts, H_Hat() loops making true the wrong return value.
>>
>> If Halts((u32)H_Hat, (u32)H_Hat) returns false to H_Hat() meaning that
>> its input halts, H_Hat() halts making false the wrong return value.
>
> Yes, So Halts gets the answer wrong, but there is a answer.
>

Because neither return value from the entire solution set of true/false
is correct the decision problem is incorrect.

>>
>> void H_Hat(u32 P)
>> {
>>   u32 Input_Halts = Halts(P, P);
>>   if (Input_Halts)
>>     HERE: goto HERE;
>> }
>>
>> int main()
>> {
>>   u32 Input_Would_Halt = Halts((u32)H_Hat, (u32)H_Hat);
>>   Output("Input_Would_Halt = ", Input_Would_Halt);
>> }
>>
>>
>> A an adapted UTM can determine whether or not an input finite string
>> represents a Turing Machine that would halt on its input without having
>> to have its simulation stopped.
>>
>
> Which isn't the question to the classical Turing Problem, so is
> meaningless to say anything about the proofs of the impossiblity to
> universally solve the Classical Halting Problem.
>

As soon as the pathological self-reference error is eliminated from the
decision problem the corrected decision problem can be decided.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein