Re: Turing computable functions

Op 27.mrt.2025 om 18:41 schreef olcott:

On 3/27/2025 5:33 AM, Fred. Zwarts wrote:

Op 26.mrt.2025 om 17:25 schreef olcott:

On 3/26/2025 2:44 AM, Mikko wrote:

On 2025-03-25 19:24:07 +0000, olcott said:
>

Cannot possibly derive any outputs not computed from
their inputs.
>
A Turing machine halt decider cannot possibly report
on the behavior of any directly executing process.

>
It can if that report is a computable function of their inputs.
For example, whether the direct execution of another Turing machine
is longer than 2 steps is Turing computable.
>

>
When an input to a simulating termination analyzer
defines a pathological relationship to its simulating
termination analyzer this changes the behavior of this
input relative to its direct execution.

 

If an analyser has a pathological relation with this input, it is wrong to choose this analyser for this input. In particular when there are analysers that do not have this relationship with this input.

 It is the input that specifies the pathological relationship.
This means that you are saying that the analyzer should reject
this input.

Yes, reject because it cannot analyse correctly.
It is not very interesting to know whether an analyser reports that it is unable to analyse the problem correctly.
It is interesting to know:
'Is there an algorithm that can determine for all possible inputs whether the input specifies a program that (according to the semantics of the machine language) halts when directly executed?'
This question seems undecidable for Olcott.