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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is Correctly rejected as
 non-halting V2
Date: Sun, 21 Jul 2024 14:55:50 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sun, 21 Jul 2024 08:34:40 -0500 schrieb olcott:
> On 7/21/2024 4:34 AM, Mikko wrote:
>> On 2024-07-20 13:11:03 +0000, olcott said:
>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>> On 2024-07-19 14:08:24 +0000, olcott said:

>> If HHH(DDD) abrots its simulation and returns true it is correct as a
>> halt decider for DDD really halts.
> (b) We know that a decider is not allowed to report on the behavior
> computation that itself is contained within. Deciders only take finite
> string inputs. They do not take executing processes as inputs. Thus HHH
> is not allowed to report on the behavior of this int main() { DDD(); }.
Its input just happens to be the same as enclosing computation.

> Although embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly correctly report on its own
> behavior because its input does the opposite of whatever it reports
> embedded_H is only allowed to report on the behavior that its input
> specifies.
Which is the opposite.

> Turing machines never take actual Turing machines as inputs.
> They only take finite strings as inputs and an actual executing Turing
> machine is not itself a finite string.
Trivial.

> Since we ourselves can directly see that UTM based embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> must abort the simulation of its input otherwise this input would never
> stop running we know that the criteria have been met.
I see that the input halts.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.