Re: No decider is ever accountable for the behavior of the computation that itself is contained within

Op 27.jul.2024 om 16:21 schreef olcott:

On 7/27/2024 2:46 AM, Mikko wrote:

On 2024-07-26 16:28:43 +0000, olcott said:
>

No decider is ever accountable for the behavior of the
computation that itself is contained within.

>
That claim is fully unjustified. How do you even define "accountable"
in the context of computations, automata, and deciders?
>

 int sum(int x, int y){ return x + y; }
sum(5,6) is not accountable for reporting sum(3,2).
It computes the mapping from its input to the value of their sum.
 HHH must compute the mapping from its input finite string
of the x86 machine code of DDD to the behavior that this
finite string specifies and then report on the halt status
of this behavior.

And the semantics of the x86 code shows that DDD has halting behaviour, which is proved by the direct execution and by the simulation by another simulator.

 The input to HHH(DDD) specifies the equivalent of infinite
recursion as fully elaborated in another reply.

The input to HHH is DDD, which includes HHH, which aborts and halts after two recursions, so DDD halts as well. Therefore, the input specifies a two cycle recursion, but HHH is unable to simulate it correctly, because
HHH cannot possibly simulate *itself* correctly, which has been proved in many replies.
Two is different from infinite. Is that already over your head?