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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets --- deciders
Date: Thu, 30 May 2024 11:55:12 -0500
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On 5/30/2024 11:13 AM, Mike Terry wrote:
> On 30/05/2024 16:21, olcott wrote:
>> On 5/30/2024 9:59 AM, Mike Terry wrote:
>>> On 30/05/2024 15:43, olcott wrote:
>>>> On 5/28/2024 11:16 AM, olcott wrote:
>>>>>
>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> *Formalizing the Linz Proof structure*
>>>>> ∃H  ∈ Turing_Machines
>>>>> ∀x  ∈ Turing_Machines_Descriptions
>>>>> ∀y  ∈ Finite_Strings
>>>>> such that H(x,y) = Halts(x,y)
>>>>>
>>>>
>>>> A decider computes the mapping from finite string inputs to
>>>> its own accept or reject state.
>>>>
>>>> A decider does not and cannot compute the mapping from
>>>> Turing_Machine inputs to its own accept or reject state.
>>>>
>>>> Halts(x,y) would report on the direct execution of x(y) thus ignores
>>>> the pathological behavior of x correctly simulated by pure function H.
>>>> This makes Halts(x,y) an incorrect measure of the correctness of 
>>>> H(x,y).
>>>>
>>>> This is easier to see when we can see every single detail of all of
>>>> the steps as an x86 execution trace of D correctly simulated by pure
>>>> function H.
>>>>
>>>> typedef int (*ptr)();  // ptr is pointer to int function in C
>>>> 00       int HH(ptr p, ptr i);
>>>> 01       int DD(ptr p)
>>>> 02       {
>>>> 03         int Halt_Status = HH(p, p);
>>>> 04         if (Halt_Status)
>>>> 05           HERE: goto HERE;
>>>> 06         return Halt_Status;
>>>> 07       }
>>>> 08
>>>> 09       int main()
>>>> 10       {
>>>> 11         HH(DD,DD);
>>>> 12         return 0;
>>>> 13       }
>>>>
>>>> *Begin simulation of DD by HH*
>>>> Begin Local Halt Decider Simulation   Execution Trace Stored at:113075
>>>> [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 ebp
>>>> [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
>>>>
>>>> DD correctly simulated by HH cannot possibly reach its own simulated
>>>> final state at line 06 in any number of steps including an infinite
>>>> number of steps because DD correctly simulated by HH remains stuck in
>>>> recursive simulation.
>>>>
>>>
>>> Your HH/DD above are nonsense functions - you have admitted that HH 
>>> uses static variables deliberately to detect whether it is the outer 
>>> (unsimulated) HH or an inner (simulated) HH.  In the event of the 
>>> latter it branches into a completely different code branch from the 
>>> outer HH, so the "simulated" behaviour of HH is /nothing like/ the 
>>> behaviour of outer HH.
>>>
>>> Any traces from such a HH/DD are completely worthless.
>>>
>>> You know this, and yet you still claim to have a "fully operational" 
>>> code etc..  So that is a LIE, just like when you claimed to have a 
>>> fully operation TM implementing your ideas a few years back.
>>>
>>>
>>> Mike.
>>
>> The fact that it uses static variables has no effect what-so-ever
>> on the fact that DD correctly simulated by HH cannot possibly
>> reach its own simulated final state at line 06.
> 
> But DD is NOT correctly simulated by HH.  HH uses static variables to 
> modify its behaviour when simulated, so the "simulation" is rubbish.
> 

Merely from the C source code it can be verified that DD correctly
simulated by pure simulator HH or pure function HH cannot possibly
reach its own simulated final state at line 06 and halt because
every DD remains stuck in recursive simulation the whole time that
it is correctly simulated.

Thus the fact that one implementation of HH is is not a pure function
makes no ultimate difference in this analysis and is a mere distraction
away from the point.

>>
>> It is very easy to verify that DD correctly simulated by HH cannot
>> possibly reach its own simulated final state and halt on the basis
>> of the execution trace that I provided and this x86 source-code for DD.
>>
>> _DD()
>> [00001c22] 55         push ebp
>> [00001c23] 8bec       mov ebp,esp
>> [00001c25] 51         push ecx
>> [00001c26] 8b4508     mov eax,[ebp+08]
>> [00001c29] 50         push eax        ; push DD
>> [00001c2a] 8b4d08     mov ecx,[ebp+08]
>> [00001c2d] 51         push ecx        ; push DD
>> [00001c2e] e80ff7ffff call 00001342   ; call HH
>> [00001c33] 83c408     add esp,+08
>> [00001c36] 8945fc     mov [ebp-04],eax
>> [00001c39] 837dfc00   cmp dword [ebp-04],+00
>> [00001c3d] 7402       jz 00001c41
>> [00001c3f] ebfe       jmp 00001c3f
>> [00001c41] 8b45fc     mov eax,[ebp-04]
>> [00001c44] 8be5       mov esp,ebp
>> [00001c46] 5d         pop ebp
>> [00001c47] c3         ret
>> Size in bytes:(0038) [00001c47]
>>
>> You are correct that HH is not a pure function yet this has no effect
>> on the provided execution trace.
> 
> Nonsense - if HH is not correctly simulating DD+HH then the trace is 
> just rubbish.
> 
> Mike.
> 

That HH is not a pure function does not show that the simulation
is incorrect because:

The simulation is proved to be correct on the basis that the x86 machine
code instructions of DD are correctly simulated by HH in the correct
order as verified by comparing the execution trace to the x86 machine
code of DD.

You merely falsely assumed that the trace was incorrect even after
I conclusively proved otherwise. Ignorance of the x86 language is no
excuse.

*Thanks again for your review*
*You are currently my best reviewer*

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer