Am Sat, 26 Jul 2025 14:10:28 -0500 schrieb olcott:
On 7/26/2025 1:46 PM, joes wrote:
Am Sat, 26 Jul 2025 12:59:35 -0500 schrieb olcott:
The error of all of the halting problem proofs is that they require a
Turing machine halt decider to report on the behavior of a directly
executed Turing machine.
It is common knowledge that no Turing machine decider can take another
directly executing Turing machine as an input, thus the above
requirement is not precisely correct.
Nobody has ever suggested that. We only care about the same behaviour
when given a description.
When we correct the error of this incorrect requirement it becomes a
Turing machine decider indirectly reports on the behavior of a
directly executing Turing machine through the proxy of a finite string
description of this machine.
HHH doesn't report on the direct execution...?
Of course it doesn't. No Turing machine based halt decider ever reports
on the behavior of the directly executed of a machine.
1. We are dealing with C functions here, not TMs.
2. An UTM/pure simulator is a semidecider for "directly" halting programs.
3. Above you required a halting decider to report on the direct execution.
HHH gives the opposite result.
--
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.
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