The truth about the halting problem counter-example input

On 7/3/2026 9:43 PM, dbush wrote:
> On 7/3/2026 10:37 PM, olcott wrote:
>> On 7/3/2026 9:19 PM, dbush wrote:
>>> On 7/3/2026 10:05 PM, olcott wrote:
>>>> On 7/3/2026 8:58 PM, dbush wrote:
>>>>> On 7/3/2026 9:52 PM, olcott wrote:
>>>>>> On 7/3/2026 5:51 PM, André G. Isaak wrote:
>>>>>>> On 2026-07-03 16:37, olcott wrote:
>>>>>>>> On 7/3/2026 1:47 PM, André G. Isaak wrote:
>>>>>>>>> On 2026-07-03 12:36, olcott wrote:
>>>>>>>>>> On 7/3/2026 1:18 PM, dbush wrote:
>>>>>>>>>
>>>>>>>>>>> If an algorithm takes an input and produces an output, that 
>>>>>>>>>>> is by definition a mapping. 
>>>>>>>>>> That only proves that the definition is incoherent.
>>>>>>>>>> The coherent way that it actually works is that
>>>>>>>>>> inputs are transformed into outputs by applying
>>>>>>>>>> finite string transformation rules to inputs to
>>>>>>>>>> derive outputs.
>>>>>>>>>
>>>>>>>>> Apparently you don't understand the difference between a 
>>>>>>>>> mapping and an algorithm. They are two different things.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> A function that ignores its input and only returns 0
>>>>>>>> is not any sort of halt function.
>>>>>>>
>>>>>>> He was defining 'mapping', not 'halt function'.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> A actual halt function must compute 
>>>>> The mathematical halting function:
>>>>>
>>>>
>>>> When you actually implement this concretely 
>>>
>>> We find that it is not possible, as Linz and others have proved.
>>>
>>
>> Impossible requirements are incorrect requirements.
>>
> 
> Nope.  Requirements are requirements for a reason.  If they can't be 
> satisfied, then that's just the way it is.
> 

The halting problem requires a decider that correctly reports the halt 
status of an input that does the opposite of whatever it reports. The 
meaning of these words prove that is logically impossible.

> I would like to have a single algorithm that can tell me whether any 
> arbitrary algorithm with a given input will halt when executed directly, 
> but unfortunately no such algorithm exists.

typedef int (*ptr)();
int HHH(ptr P);

01 int DD()
02 {
03   int Halt_Status = HHH(DD);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 void main()
10 {
11   DD();
12   HHH(DD);
13 }

HHH is not accountable to report on the
behavior of its caller on line 11.

HHH does correctly report on the behavior
that its input specifies of its on line 12.
https://github.com/plolcott/x86utm/blob/master/Halt7.c

-- 
Copyright 2026 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.

The entire body of knowledge expressed in language is
comprised of two types of relations between finite strings:
(a) *Axioms* Expressions of language that are stipulated to be true.

My system bridges the analytic/synthetic distinction by
expressly encoding all empirical "atomic facts" in a formal
language such as CycL of the Cyc project.

(b) *Inference Rules* Expressions of language that are semantically
entailed syntactically from (a) and/or (b).