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On 8/21/2024 1:30 PM, Fred. Zwarts wrote:You keep missing the idea that HHH must predict the behaviour of its input (the HHH that does a partial simulation), not the behaviour of a different hypothetical non-input (the HHH that never aborted).Op 21.aug.2024 om 14:30 schreef olcott:You keep missing the idea that HHH does a partialOn 8/21/2024 3:01 AM, Mikko wrote:>On 2024-08-21 03:01:38 +0000, olcott said:>>>
*We are only talking about one single point*
Professor Sipser must have understood that an HHH(DDD)
that does abort is supposed predict what would happen
if it never aborted.
Professor Sipser understood that what is not a part of the text
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.
>
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
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
Which is only complete if it includes all functions called by D.
Including the H that has the same behaviour as the simulating H.
>(b) As measured by the correct partial simulation of D by H>
Which does not really give a clue, because either a full simulation is needed, or an algorithm that detects non-halting.
>(c) When H would never abort its simulation of F>
No, it must predict the behaviour of the input, including the H that makes a partial simulation, not the behaviour of a hypothetical non- input that does not abort. This means to predict the behaviour of the D with the H that is called by D with the same behaviour as the simulating H. No cheating with a Root variable to give the simulated H a behaviour different from the simulating H.
>(d) This includes H simulating itself simulating D>
Itself, means the H with the same behaviour as the simulating H, i.e. doing a partial simulation.
>
Anything else is cheating and making a prediction for a non-input.
simulation of DDD to predict what would happen if
this HHH never aborted its simulation of DDD.
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