Re: My reviewers think that halt deciders must report on the behavior of their caller

Op 05.jun.2025 om 06:33 schreef olcott:

On 6/4/2025 10:41 PM, dbush wrote:

On 6/4/2025 11:32 PM, olcott wrote:

On 6/4/2025 9:56 PM, dbush wrote:

On 6/4/2025 10:44 PM, olcott wrote:

On 6/4/2025 9:13 PM, dbush wrote:

On 6/4/2025 10:09 PM, olcott wrote:

On 6/4/2025 8:43 PM, Richard Damon wrote:

On 6/4/25 11:50 AM, olcott wrote:

On 6/4/2025 2:04 AM, Mikko wrote:

On 2025-06-03 21:39:46 +0000, olcott said:
>

They all say that HHH must report on the behavior of
direct execution of DDD()

>
No, they don't say that. A halting decider (and a partial halting
decider when it reports) must report whether the direct execution
of the computation asked about terminates. Unless that computation
happens to be DDD() it must report about another behaviour instead
of DDD().
>

yet never bother to notice that the directly executed DDD() is
the caller of HHH(DDD).

>
To say that nobody has noticed that is a lie. Perhaps they have not
mentioned what is irrelevant to whatever they said. In particular,
whether DDD() calls HHH(DDD) is irrelevant to the requirement that
a halting decider must report about a direct exection of the
computation the input specifies.
>

>
*People have ignored this for 90 years*
*People have ignored this for 90 years*
*People have ignored this for 90 years*
>
The only possible way that HHH can report on the
direct execution of DDD() is for HHH to report on
the behavior of its caller:

>
So?
>
It *IS* a fact that to be correct, it needs to answer about the direct executiom of the program that input represents.
>
That is DEFINITION.
>

>
Likewise with the definition of Russell's Paradox
until ZFC showed that this definition is complete
nonsense.
>

>
But unlike Russel's Paradox, which showed a contradiction in the axioms of naive set theory, there is no contradiction in the axioms of computation theory.  It follows from those axioms that no H exists that performs the below mapping, as you have *explicitly* agreed.
>

>
int main()
{
   DDD(); // comp theory does not allow HHH to
}        // report on the behavior of its caller.
>

>
>
int main()
{
    DDD();     // this
    HHH(DDD);  // is not the caller of this: this is }              // asking what the above will do

>
That is just not the way that computation actually works.

>
Sure it is.  We don't care how the mapping is generated, only that it is generated.
>

>
There is not enough information in the input to
know how the caller works.

 Counterfactual. The input is a pointer to the start of a function.

The code of that function has addresses to other functions used in the program, including the code that aborts and halts.
All information is there. But the programmer of HHH decided to make HHH such that it does not see all the information. It is a choice to analyse only the code of DDD itself. A wrong choice. It should also analyse the code of the functions called by DDD. Including the conditional branch instructions within the functions called by DDD.
 

>
Also there is not enough information in any integer
to predict who the president will be.
>
char* WhatIsTheNameOfThePresidentIn2030(int x);

 Irrelevant, because the pointer given to HHH is enough to find all information, which is proven by the fact that world-class simulator give the correct result when given exactly the same pointer as input.