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Before we can get to the behavior of the directly executedBut it hasn't since the Sipser criteria is based on "Correct SImulation" meaning a simulation the exactly reproduces the behavior of the directly executed code, which means a simulation that doesn't stop until it reaches a final state (even if that takes forever).
DD(DD) we must first see that the Sipser approved criteria
have been met:
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
If simulating halt decider H correctly simulates its input D
until H correctly determines that its simulated D would never
stop running unless aborted then
H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words10/13/2022>
On 10/14/2022 7:44 PM, Ben Bacarisse wrote:And why do we care?
> I don't think that is the shell game. PO really /has/ an H
> (it's trivial to do for this one case) that correctly determines
> that P(P) *would* never stop running *unless* aborted.
Try to show how this DD correctly simulated by any HH ever
stops running without having its simulation aborted by HH.
_DD()Nope, by your definition
[00001e12] 55 push ebp
[00001e13] 8bec mov ebp,esp
[00001e15] 51 push ecx
[00001e16] 8b4508 mov eax,[ebp+08]
[00001e19] 50 push eax ; push DD
[00001e1a] 8b4d08 mov ecx,[ebp+08]
[00001e1d] 51 push ecx ; push DD
[00001e1e] e85ff5ffff call 00001382 ; call HH
A {correct simulation} means that each instruction of the
above x86 machine language of DD is correctly simulated
by HH and simulated in the correct order.
In other words the first seven steps of DD correctly simulated
by HH call HH(DD,DD) to repeat these first seven steps. HH then
simulates itself simulating DD until this second instance of DD
calls another HH(DD,DD) to repeat these first seven steps again.
New slave_stack at:10306dAnd this does not happen by your definition of a correst simulation, but the trace SHOULD continue at address 00001342, and show the code of HH
Begin Local Halt Decider Simulation Execution Trace Stored at:113075
machine stack stack machine assembly
address address data code language
======== ======== ======== ========= =============
[00001c22][00113061][00113065] 55 push ebp
[00001c23][00113061][00113065] 8bec mov ebp,esp
[00001c25][0011305d][00103031] 51 push ecx
[00001c26][0011305d][00103031] 8b4508 mov eax,[ebp+08]
[00001c29][00113059][00001c22] 50 push eax ; push DD
[00001c2a][00113059][00001c22] 8b4d08 mov ecx,[ebp+08]
[00001c2d][00113055][00001c22] 51 push ecx ; push DD
[00001c2e][00113051][00001c33] e80ff7ffff call 00001342 ; call HH
New slave_stack at:14da95
[00001c22][0015da89][0015da8d] 55 push ebpNope, it shows that you can't even follow your own definitions.
[00001c23][0015da89][0015da8d] 8bec mov ebp,esp
[00001c25][0015da85][0014da59] 51 push ecx
[00001c26][0015da85][0014da59] 8b4508 mov eax,[ebp+08]
[00001c29][0015da81][00001c22] 50 push eax ; push DD
[00001c2a][0015da81][00001c22] 8b4d08 mov ecx,[ebp+08]
[00001c2d][0015da7d][00001c22] 51 push ecx ; push DD
[00001c2e][0015da79][00001c33] e80ff7ffff call 00001342 ; call HH
Local Halt Decider: Recursive Simulation Detected Simulation Stopped
The above is the complete proof that DD correctly simulated
by any HH that can possibly exist never stops running without
having its simulation aborted by HH (or crashing for OOM error).
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