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On 3/9/24 10:33 AM, olcott wrote:It is a verified fact that when H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ meet this criteria that H gets the right answer and Ĥ.H gets the wrong answer.*Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior*Specifications, not actual behavior until the existance of such an H is shown.
>
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
IF taken as actual behavior, then it is conditional on such an H existing.
>It NEEDS to in order to meet its specification
Execution trace of Ĥ applied to ⟨Ĥ⟩
(a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H
(b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
(c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process
*This proves that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ must abort its simulation*
It DOESN'T unless its algorithm says it does,
If it just fails to answer, then it has failed to be a correct Halt Decider.
The fact that you reach this conflict in actions, is the reason Halt Deciding is uncomputable.
>In other words, you are admitting to changing the question, and thus LYING that you are working on the actual original problem.
*This is a verified fact*
When simulating halt deciders always report on the behavior of
their simulated input from their own POV then when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
transitions to Ĥ.Hqn it is correct from its own POV.
>Which just means you are LYING that this apply to an actual Halt Decider per the Halting Theory,
*This is a verified fact*
When that occurs then H ⟨Ĥ⟩ ⟨Ĥ⟩ would transition to H.qy from
its own POV.
>And thus you are admitting that the H in H^.H is WRONG and thus H is not a correct Halt Decider, because it gets some cases wrong.
When Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ report on the basis of their own
POV then Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ reports incorrectly about the behavior of
Ĥ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ reports the behavior of Ĥ ⟨Ĥ⟩ correctly.
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