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

On 6/5/2025 6:19 AM, Richard Damon wrote:

On 6/5/25 12:33 AM, olcott wrote:

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.

 The the input isn't complete, and you did your problem wrong.
 

The actual input specifies a sequence of configurations
that cannot possibly reach their own final halt state.
The caller is *not* the input.
To say that its caller is its input is the same
as saying that you are your mother's father.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer