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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: No decider is ever accountable for the behavior of the
 computation that itself is contained within
Date: Fri, 26 Jul 2024 12:29:49 -0500
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On 7/26/2024 12:09 PM, olcott wrote:
> On 7/26/2024 11:28 AM, olcott wrote:
>> No decider is ever accountable for the behavior of the
>> computation that itself is contained within.
>>
>> It is only accountable for computing the mapping from the
>> input finite string to the actual behavior that this finite
>> string specifies.
>>
>> typedef void (*ptr)();
>> int HHH(ptr P);
>>
>> void DDD()
>> {
>>    HHH(DDD);
>> }
>>
>> int main()
>> {
>>    DDD();
>> }
>>
>> HHH(DDD) is only accountable for the actual behavior that
>> its input specifies and is not accountable for the behavior
>> of the computation that itself is contained within:
>> the directly executed DDD();
>>
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> (a) Ĥ copies its input ⟨Ĥ⟩
>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
>> (g) goto (d) with one more level of simulation
>>
>> Two complete simulations show a pair of identical TMD's are
>> simulating a pair of identical inputs.  We can see this thus
>> proving recursive simulation.
>>
>> When we understand that embedded_H is accountable for the
>> behavior of its input and not accountable for the behavior
>> of the computation that itself is contained within then
>> we understand that embedded_H is necessarily correct to
>> transition to its own Ĥ.qn state.
>>
>> https://www.liarparadox.org/Linz_Proof.pdf
>>
>>
> _DDD()
> [00002177] 55               push ebp
> [00002178] 8bec             mov ebp,esp
> [0000217a] 6877210000       push 00002177 ; push DDD
> [0000217f] e853f4ffff       call 000015d7 ; call HHH
> [00002184] 83c404           add esp,+04
> [00002187] 5d               pop ebp
> [00002188] c3               ret
> Size in bytes:(0018) [00002188]
> 
> _main()
> [00002197] 55               push ebp
> [00002198] 8bec             mov ebp,esp
> [0000219a] e8d8ffffff       call 00002177 ; call DDD
> [0000219f] 33c0             xor eax,eax
> [000021a1] 5d               pop ebp
> [000021a2] c3               ret
> Size in bytes:(0012) [000021a2]
> 
>   machine   stack     stack     machine    assembly
>   address   address   data      code       language
>   ========  ========  ========  =========  =============
> [00002197][001037e9][00000000] 55         push ebp
> [00002198][001037e9][00000000] 8bec       mov ebp,esp
> [0000219a][001037e5][0000219f] e8d8ffffff call 00002177 ; call DDD
> [00002177][001037e1][001037e9] 55         push ebp
> [00002178][001037e1][001037e9] 8bec       mov ebp,esp
> [0000217a][001037dd][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][001037d9][00002184] e853f4ffff call 000015d7 ; call HHH
> 


> // executed HHH emulates 1st instance of DDD
> New slave_stack at:10388d
> Begin Local Halt Decider Simulation   Execution Trace Stored at:113895
> [00002177][00113885][00113889] 55         push ebp
> [00002178][00113885][00113889] 8bec       mov ebp,esp
> [0000217a][00113881][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][0011387d][00002184] e853f4ffff call 000015d7 ; call HHH
> 
> // emulated HHH emulates 2nd instance of DDD
> New slave_stack at:14e2b5
> [00002177][0015e2ad][0015e2b1] 55         push ebp
> [00002178][0015e2ad][0015e2b1] 8bec       mov ebp,esp
> [0000217a][0015e2a9][00002177] 6877210000 push 00002177 ; push DDD
> [0000217f][0015e2a5][00002184] e853f4ffff call 000015d7 ; call HHH
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
> 

The above has the same behavior pattern as infinite recursion
shown below.

void Infinite_Recursion()
{
   Infinite_Recursion();
}

_Infinite_Recursion()
[0000215a] 55               push ebp
[0000215b] 8bec             mov ebp,esp
[0000215d] e8f8ffffff       call 0000215a ; recursive call
[00002162] 5d               pop ebp
[00002163] c3               ret
Size in bytes:(0010) [00002163]

Begin Local Halt Decider Simulation   Execution Trace Stored at:113934
[0000215a][00113924][00113928] 55               push ebp
[0000215b][00113924][00113928] 8bec             mov ebp,esp
[0000215d][00113920][00002162] e8f8ffffff       call 0000215a
[0000215a][0011391c][00113924] 55               push ebp
[0000215b][0011391c][00113924] 8bec             mov ebp,esp
[0000215d][00113918][00002162] e8f8ffffff       call 0000215a
Local Halt Decider: Infinite Recursion Detected Simulation Stopped


> [00002184][001037e1][001037e9] 83c404     add esp,+04
> [00002187][001037e5][0000219f] 5d         pop ebp
> [00002188][001037e9][00000000] c3         ret
> [0000219f][001037e9][00000000] 33c0       xor eax,eax
> [000021a1][001037ed][00000018] 5d         pop ebp
> [000021a2][001037f1][00000000] c3         ret
> Number of Instructions Executed(10071) == 150 Pages
> 



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