Re: embedded_H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ incorrectly computes the mapping from its input to Ĥ.qn

On 8/2/24 8:47 AM, olcott wrote:

On 8/2/2024 1:28 AM, Mikko wrote:

On 2024-08-01 11:49:13 +0000, olcott said:
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On 8/1/2024 2:44 AM, Mikko wrote:

On 2024-07-31 17:27:33 +0000, olcott said:
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On 7/31/2024 2:32 AM, Mikko wrote:

On 2024-07-30 14:16:20 +0000, olcott said:
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On 7/30/2024 1:37 AM, Mikko wrote:

On 2024-07-29 16:16:13 +0000, olcott said:
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On 7/28/2024 3:02 AM, Mikko wrote:

On 2024-07-27 14:08:10 +0000, olcott said:
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On 7/27/2024 2:21 AM, Mikko wrote:

On 2024-07-26 14:08:11 +0000, olcott said:
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When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

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The above is merely simplified syntax for the top of page 3
https://www.liarparadox.org/Linz_Proof.pdf
The above is the whole original Linz proof.

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And even more simplified semantics.
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(a) Ĥ copies its input ⟨Ĥ⟩
(b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
(e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
(f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
(g) goto (d) with one more level of simulation
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You are supposed to evaluate the above as a contiguous
sequence of moves such that non-halting behavior is
identified.

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The above is an obvious tight loop of (d), (e), (f), and (g).
Its relevance (it any) to the topic of the discussion is not
obvious.
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When we compute the mapping from the input to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
to the behavior specified by this input we know that embedded_H
is correct to transition to Ĥ.qn.

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The meaning of "correct" in this context is that if the transition of
embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qn is correct if H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn but
incorrect otherwise.

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No you are wrong.

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Which dictionary (or other authority) disagrees?

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Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function
is computable if there exists an algorithm that can do the
job of the function, i.e. *given an input of the function*
*domain it can return the corresponding output*
https://en.wikipedia.org/wiki/Computable_function
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The common knowledge that a decider computes the mapping
from its input finite string...
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This is almost always the same as the direct execution of
the machine represented by this finite string.

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None of above indicates any disagreement by any authority.
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Everyone (even Linz) has the wrong headed idea that a halt
decider must report on the behavior of the computation that
itself is contained within. This has always been wrong.

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What does "must" mean above? How does that relate to what Linz
really says?
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 A decider computes the mapping from a finite string.
A decider does not compute the mapping from an execution machine.
 

A halt decider must always report on the behavior that its
finite string specifies. This is different only when an
input invokes its own decider.

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The input string cannot "invoke". It only specifies.
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 In the x86 language emulated DDD calls and emulated HHH(DDD).
The same thing occurs when Linz Ĥ ⟨Ĥ⟩ transitions to embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩.
 This is repeated with simulated ⟨Ĥ⟩ instances transitioning to
simulated instances of embedded_H.
 

And, since embedded_H and HHH will decide to abort their emulations and return, a correct emulation of them will show that, even if the PARTIAL emulation done by them can not reach that point.
The routines are what they are and the correct emulation will show that behavior. A version of HHH looking at an input that calls itself, but treating it as a non-aborting version of itself isn't looking at the input given to it.
If HHH properly emulates the code of HHH that it sees, it will see the conditional instructions that tells it there is at least a possibility of this program terminating, so it can't just use the loop with no conditional rule for non-termination.
Your attempting to do so just proves your utter stupidity, and the fact you repeat the error after it has been pointed out makes you a pathological liar.