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On 8/21/2024 3:01 AM, Mikko wrote:From the meaning of "halt decider H" follows that the behaviour isOn 2024-08-21 03:01:38 +0000, olcott said:<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>*We are only talking about one single point*Professor Sipser understood that what is not a part of the text
Professor Sipser must have understood that an HHH(DDD)
that does abort is supposed predict what would happen
if it never aborted.
is not a part of the agreement. What H is required to predict
is fully determined by the words "halt decider H". The previous
word "simulating" refers to an implementation detail and does
not affect the requirements.
If simulating halt decider H correctly simulates its input D
until H correctly determines that its simulated D would never
stop running unless aborted then
H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
It is crucial to the requirements in that it specifies that
H is required to predict
(a) The behavior specified by the finite string D
(b) As measured by the correct partial simulation of D by HThe counterfactual assumption that H would never aboort does not
(c) When H would never abort its simulation of F
(d) This includes H simulating itself simulating D
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