Re: How do computations actually work?

On 5/24/2025 12:06 PM, olcott wrote:

On 5/24/2025 10:15 AM, dbush wrote:

On 5/24/2025 11:13 AM, olcott wrote:

On 5/24/2025 2:39 AM, Mikko wrote:

On 2025-05-23 16:10:19 +0000, olcott said:
>

On 5/23/2025 2:14 AM, Mikko wrote:

On 2025-05-23 03:31:15 +0000, olcott said:
>

On 5/22/2025 10:23 PM, wij wrote:

On Thu, 2025-05-22 at 21:47 -0500, olcott wrote:

[cut]

>
Q: How do computations actually work?
A: Computation is merely step-by-step algorithm.
Nothing says it has to be TM.
>
Do the exercises in textbooks first before any claim of it.
>

>
int main()
{
   DD(); // by what steps can the HHH that DD calls
}       // report on the behavior its caller?

>
If we don't insist that the report be correct:
1. guess
2. tell what was guessed

>
This does not work because all computable functions
that implement termination analyzers must compute
the mapping from their input finite string according
to the behavior that it specifies.

>
Wrong. There is no need to compute "the" mapping if a the report
needs not be correct. Some other mapping is enough to produce
some report.
>

>
int sum(int x, int y) { return 5; }
Does not compute any function because it ignores its inputs.
>

>
Sure it does.  It computes this function:
>
>
For all integers X and Y:
>
(X,Y) maps to 5
>
>
The only requirements for mapping is a function is that inputs correspond to outputs as per the given mapping, and the mathematical function above is mapped by the above C function "sum".

 OK
 int main()
{
   DD(); // How does the HHH that DD calls report on the
}       // actual behavior of its actual caller?
 

It doesn't matter, as your HHH doesn't accept a description of an algorithm as input and therefore has nothing to do with the halting problem, as you yourself have admitted:
On 5/13/2025 9:54 PM, dbush wrote:
 > On 5/13/2025 9:48 PM, olcott wrote:
 >> On 5/13/2025 8:31 PM, dbush wrote:
 >>> On 5/13/2025 9:27 PM, olcott wrote:
 >>>> On 5/13/2025 8:07 PM, dbush wrote:
 >>>>> On 5/13/2025 5:30 PM, olcott wrote:
 >>>>>> On 5/13/2025 6:43 AM, Richard Damon wrote:
 >>>>>>> On 5/13/25 12:52 AM, olcott wrote:
 >>>>>>>> *simulated D would never stop running unless aborted*
 >>>>>>>> or they themselves could become non-terminating.
 >>>>>>>
 >>>>>>> But you aren't simulating the same PROGRAM D that the original
 >>>>>>> was given.
 >>>>>>>
 >>>>>>
 >>>>>> It is not supposed to be the same program.
 >>>>>
 >>>>> So you *explicitly* admit to changing the input.
 >>>>>
 >>>>
 >>>> The finite string of DD is specific sequence bytes.
 >>>
 >>> Which includes the specific sequence of bytes that is the finite
 >>> string HHH
 >>>
 >>
 >> No it does not. A function calls is not macro inclusion.
 >>
 >
 > Then you admit that your HHH not deciding about algorithms and therefore
 > has nothing to do with the halting problem.