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

On 11/6/2021 3:46 PM, André G. Isaak wrote:

On 2021-11-06 11:52, olcott wrote:

The brand new exception to the rule that the pure simulation of a
machine description on its input and the direct execution of this
machine on its input ARE COMPUTATIONALLY EQUIVALENT is the case where
the decider and its machine description input have a pathological
relationship to each other.

And you justify this incoherent claim how exactly?

The actual pure simulation of the first 14 steps of the x86 machine
language input to H(P,P) conclusively proves beyond all possible doubt
that H(P,P)==0 is correct even of H never returns.

You won't be able to understand what I am saying until after you
comprehend this fact. Ben is hopelessly lost because he is utterly
clueless about the x86 language, perhaps you too are utterly clueless
about the x86 language.

If the pure simulation isn't computationally equivalent to the direct execution, in what possible sense is it a 'pure simulation'?

I have told you this too many times.

When each instruction of the x86 source code is simulated in the exact
same sequence that it is specified in the source code we know that this
aspect of the simulation is perfectly correct.

We also know that when H is a pure simulator of its input that the
seventh line of the correct pure simulation execution trace shown below
would result in another identical sequence.

machine stack stack machine assembly
address address data code language
======== ======== ======== ========= ============= [00000c36][002117ca][002117ce] 55 push ebp [00000c37][002117ca][002117ce] 8bec mov ebp,esp [00000c39][002117ca][002117ce] 8b4508 mov eax,[ebp+08] [00000c3c][002117c6][00000c36] 50 push eax // push P [00000c3d][002117c6][00000c36] 8b4d08 mov ecx,[ebp+08] [00000c40][002117c2][00000c36] 51 push ecx // push P [00000c41][002117be][00000c46] e820fdffff call 00000966 // call H(P,P)

We don't need to see the 350 pages of the simulation of H to know that
if this H does a pure simulation of its input that the above seven lines
will be repeated in the subsequent nested simulation.

And if your 'simulating halt decider' is simulating something which is
not computationally equivalent to the computation described by its
input, then in what possible sense is it actually answering a question
about its input?

P(P) halts. A halt decider must therefore claim that it halts. If it
decides that some simulation which is not computationally equivalent to
P(P) doesn't halt then it isn't answering about its input, which means
it isn't a halt decider at all.

André

--
Copyright 2021 Pete Olcott

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

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