XPost: comp.theory, sci.logic, sci.math

On 12/31/2021 7:37 PM, André G. Isaak wrote:

On 2021-12-31 18:17, olcott wrote:

On 12/31/2021 7:11 PM, André G. Isaak wrote:

On 2021-12-31 17:05, olcott wrote:

On 12/31/2021 5:33 PM, André G. Isaak wrote:

On 2021-12-31 16:02, olcott wrote:

On 12/31/2021 4:06 PM, André G. Isaak wrote:

An actual computer scientist will understand that embedded_H does
compute the mapping from these inputs finite strings ⟨Ĥ⟩ ⟨Ĥ⟩ to
this final state Ĥ.qn on the basis that the actual input would
never halt.

You're not really in a position to state what an actual computer
scientist would understand. Only an actual computer scientist can
do that.

It is a self-evident truth that:
(a) The pure simulation of the Turing machine description of a
machine is computationally equivalent to the direct execution of
this machine.

(b) The pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would never halt.

(c) If the pure simulation of the input to a halt decider would
never halt then the halt decider correctly decides that this input
does not halt.

A computer scientist would understand these things.

It would appear that you ignored (and cut) all the actual points in
my post.

Why don't we simplify things a bit. When Ĥ ⟨Ĥ⟩ is called, how does Ĥ >>> determine that its input describes itself? You claim this is done by
string comparisons, but which strings are being compared? The only
string Ĥ has access to its input string. What does it compare this
string with?

André

So far I have not gotten to any point of closure on anything that I
have said. I must insist on points of closure for continued dialogue.

Do you agree that the pure simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H would
never halt?

Of course I don't, since that claim is simply false.

Now why don't you actually answer the question I asked?

André

For simplicity we will refer to the copy of Linz H at Ĥ.qx embedded_H.

Simplified syntax adapted from bottom of page 319:
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

If embedded_H would never stop simulating its input ⟨Ĥ⟩ ⟨Ĥ⟩
this input would never reach a final state and stop running.

These steps would keep repeating:
Ĥ copies its input ⟨Ĥ⟩ to ⟨Ĥ⟩ then embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩...

computation that halts
...the Turing machine will halt whenever it enters a final state (Linz:1990:234)

That you disagree with self-evident truth proves that you do not want
any honest dialogue.



--
Copyright 2021 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

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