Re: DDD correctly emulated by HHH is Correctly rejected as non-halting V2

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.

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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.