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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: No decider is ever accountable for the behavior of the
 computation that itself is contained within
Date: Sat, 27 Jul 2024 21:01:13 +0200
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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?