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

On 11/4/2021 4:23 PM, André G. Isaak wrote:

On 2021-11-04 15:20, olcott wrote:

On 11/4/2021 3:09 PM, Malcolm McLean wrote:

On Thursday, 4 November 2021 at 17:41:31 UTC, André G. Isaak wrote:

(1) The above 14 simulated lines are a correct pure simulation of the >>>>> input to H(P,P) for every possible encoding of simulating halt
decider H.

What exactly does 'every possible encoding of simulating halt
decider H'
even mean?

You need to understand the PO is working with x86 code, not Turing
machines.
So P does not contain an embedded near copy of H, as in Linz's scheme,
but a call to H.
Now at first sight, that doesn't matter. But it allows for a mental
separation
between "the input" (the simple little driver which calls H and
inverts behaviour
when it gets the result)  and H itself (the halt decider).
If we replace the call to H by a call to another simulating halt
decider, have
we changed anything now?

I think that you have this correctly.

My current proof applies to every possible encoding of H thus
eliminating any need to see the encoding of any specific H.

Again, I ask, what do you mean by an 'encoding of H'?

The C source code. H can be written an infinite number of different ways
and each one of these ways would derive the exact same pure simulation
of its input.

Since my new proof doesn't care about whether or not H decides its input correctly we don't need to examine the details of how H makes its halt
status decision.

My new proof merely shows that a pure simulation of the input to H(P,P)
never reaches the final state of P, therefore not halting would be a
correct halt status decision.


--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

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