Re: How do computations actually work?

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

On 2025-05-23 03:31:15 +0000, olcott said:
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On 5/22/2025 10:23 PM, wij wrote:

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

[cut]

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Q: How do computations actually work?
A: Computation is merely step-by-step algorithm.
Nothing says it has to be TM.
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Do the exercises in textbooks first before any claim of it.
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int main()
{
   DD(); // by what steps can the HHH that DD calls
}       // report on the behavior its caller?

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

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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.

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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.
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 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".