Re: The truth about the halting problem counter-example input

On 7/6/2026 3:07 AM, Mikko wrote:
> On 04/07/2026 20:16, olcott wrote:
>> On 7/4/2026 3:58 AM, Mikko wrote:
>>> On 04/07/2026 06:11, olcott wrote:
>>>> 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.
>>>
>>> It is if HHH reagards itself as a part of the input. 
>>
>> There is no regarding to it
>> HHH is not accountable to report on the
>> behavior of its caller on line 11.
> 
> Yes, there is. If HHH interpretes the call to HHH as a call

You did not bother to pay attention to the line number 11.
The HP stupidly assumes that a halt function must report
on the behavior its caller. HHH has no access to its caller.

> to itself then it must regard itself as a part of the input.
> Otherwise it must interprete HHH as a call to some function
> other than itself, so it must regard itself as not a part of
> the input. EIther way, it must report correcltly about the
> behaviour as obsservable in an execution of the computation
> specified by the input.
> 
> Of course this is irrelevant to the Turing machine halting problem.
> A Turing machine never calls another Turing machine.
> 


-- 
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).