On 2/11/2023 2:54 PM, olcott wrote:
> On 2/11/2023 10:17 AM, olcott wrote:
>> On 2/11/2023 9:29 AM, olcott wrote:
>>> On 2/10/2023 10:03 PM, olcott wrote:
>>>> On 2/10/2023 6:29 PM, olcott wrote:
>>>>> On 2/10/2023 5:46 PM, olcott wrote:
>>>>>> Every E correctly simulated by any HH cannot possibly halt
>>>>>> (AKA reach its own return instruction and terminate normally)
>>>>>>
>>>>>> void E(int (*x)())
>>>>>> {
>>>>>>    HH(x, x);
>>>>>>    return;
>>>>>> }
>>>>>>
>>>>>> int main()
>>>>>> {
>>>>>>    HH(E,E);
>>>>>> }
>>>>>>
>>>>>> _E()
>>>>>> [00001d40] 55             push ebp
>>>>>> [00001d41] 8bec           mov ebp,esp
>>>>>> [00001d43] 8b4508         mov eax,[ebp+08]
>>>>>> [00001d46] 50             push eax
>>>>>> [00001d47] 8b4d08         mov ecx,[ebp+08]
>>>>>> [00001d4a] 51             push ecx
>>>>>> [00001d4b] e820f6ffff     call 00001370
>>>>>> [00001d50] 83c408         add esp,+08
>>>>>> [00001d53] 5d             pop ebp
>>>>>> [00001d54] c3             ret
>>>>>> Size in bytes:(0021) [00001d54]
>>>>>>
>>>>>> _main()
>>>>>> [00001d60] 55             push ebp
>>>>>> [00001d61] 8bec           mov ebp,esp
>>>>>> [00001d63] 68401d0000     push 00001d40
>>>>>> [00001d68] 68401d0000     push 00001d40
>>>>>> [00001d6d] e8fef5ffff     call 00001370
>>>>>> [00001d72] 83c408         add esp,+08
>>>>>> [00001d75] 33c0           xor eax,eax
>>>>>> [00001d77] 5d             pop ebp
>>>>>> [00001d78] c3             ret
>>>>>> Size in bytes:(0025) [00001d78]
>>>>>>
>>>>>>   machine   stack     stack     machine    assembly
>>>>>>   address   address   data      code       language
>>>>>>   ========  ========  ========  =========  =============
>>>>>> [00001d60][00103017][00000000] 55         push ebp
>>>>>> [00001d61][00103017][00000000] 8bec       mov ebp,esp
>>>>>> [00001d63][00103013][00001d40] 68401d0000 push 00001d40
>>>>>> [00001d68][0010300f][00001d40] 68401d0000 push 00001d40
>>>>>> [00001d6d][0010300b][00001d72] e8fef5ffff call 00001370
>>>>>> New slave_stack at:1030bb
>>>>>>
>>>>>> Begin Local Halt Decider Simulation   Execution Trace Stored
>>>>>> at:1130c3
>>>>>> [00001d40][001130af][001130b3] 55         push ebp      // begin E
>>>>>> [00001d41][001130af][001130b3] 8bec       mov ebp,esp
>>>>>> [00001d43][001130af][001130b3] 8b4508     mov eax,[ebp+08]
>>>>>> [00001d46][001130ab][00001d40] 50         push eax      // push
>>>>>> address of E
>>>>>> [00001d47][001130ab][00001d40] 8b4d08     mov ecx,[ebp+08]
>>>>>> [00001d4a][001130a7][00001d40] 51         push ecx      // push
>>>>>> address of E
>>>>>> [00001d4b][001130a3][00001d50] e820f6ffff call 00001370 // call HH
>>>>>> New slave_stack at:14dae3
>>>>>> [00001d40][0015dad7][0015dadb] 55         push ebp      // begin E
>>>>>> [00001d41][0015dad7][0015dadb] 8bec       mov ebp,esp
>>>>>> [00001d43][0015dad7][0015dadb] 8b4508     mov eax,[ebp+08]
>>>>>> [00001d46][0015dad3][00001d40] 50         push eax      // push
>>>>>> address of E
>>>>>> [00001d47][0015dad3][00001d40] 8b4d08     mov ecx,[ebp+08]
>>>>>> [00001d4a][0015dacf][00001d40] 51         push ecx      // push
>>>>>> address of E
>>>>>> [00001d4b][0015dacb][00001d50] e820f6ffff call 00001370 // call HH
>>>>>> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>>>>>>
>>>>>> [00001d72][00103017][00000000] 83c408     add esp,+08
>>>>>> [00001d75][00103017][00000000] 33c0       xor eax,eax
>>>>>> [00001d77][0010301b][00000018] 5d         pop ebp
>>>>>> [00001d78][0010301f][00000000] c3         ret
>>>>>> Number of Instructions Executed(15319) == 229 Pages
>>>>>>
>>>>>
>>>>> Because Every E correctly simulated by any HH cannot possibly halt any
>>>>> HH that detects this is correct to abort its simulation and reject its
>>>>> input as non-halting.
>>>>>
>>>>> No halt decider is ever required to simulate any number of steps of
>>>>> its
>>>>> input. Halt deciders are only required to correctly predict whether or
>>>>> not their input can possibly reach its own final state and terminate
>>>>> normally.
>>>>>
>>>>> Simulating halt decider HH computes the mapping from its input E to an
>>>>> accept or reject state on the basis of the behavior of E correctly
>>>>> simulated by HH. As soon as HH has simulated enough steps of E to
>>>>> correctly predict that E cannot possibly reach its own final state
>>>>> then
>>>>> HH is correct to abort its simulation of E and reject E as
>>>>> non-halting.
>>>>>
>>>>>
>>>>
>>>> When we have examined every element of the infinite set of HH/E pairs
>>>> and and found that no E correctly simulated by HH ever halts then it is
>>>> necessarily correct for HH(E,E) to reject its input as non-halting.
>>>>
>>>> When we find a pea under every shell of the shell game then it is
>>>> impossible to do a switch-a-roo and hide the pea under a different
>>>> shell. https://en.wikipedia.org/wiki/Shell_game
>>>>
>>>
>>> ∀HH ∈ (E is correctly simulated by H) (¬∃(HH/E pair) Halts(E))
>>> ∴ HH(E,E)==0 is correct for every HH that aborts its simulation of E.
>>>
>>> HH only needs to simulate E until HH correctly detects that E has a
>>> repeating state such that E correctly simulated by HH cannot possibly
>>> reach its own final state an terminate normally.
>>>
>>> Simulating halt deciders must compute the mapping from their inputs to
>>> their own accept or reject state on the basis of their correct
>>> simulation of their input up to the point when they correctly determine
>>> that E correctly simulated by HH cannot possibly reach its own final
>>> state an terminate normally.
>>>
>>> In the same way that Sum(3,4) must compute the sum of 3+4 and is not
>>> allowed to compute the sum of 2+6 HH is only allowed to report on the
>>> behavior of E simulated by HH. As soon as HH correctly detects that E
>>> has a repeating state HH is correct to abort its simulation and reject
>>> its input as non-halting.
>>>
>>
>> HH only needs to simulate E until HH correctly detects that E has a
>> repeating state such that E correctly simulated by HH cannot possibly
>> reach its own final state an terminate normally in any finite number of
>> steps.
>>
>
> Two people with masters degrees in computer science have agreed that E
> correctly simulated by HH cannot possibly reach its own "return"
> instruction in any finite number of steps of correct simulation.
>
> Since this is such simple software engineering it seems to me that
> anyone disagreeing knows this too and is simply lying.
>

Because E correctly simulated by HH cannot possibly reach its own
"return" instruction in any finite number of steps HH is necessarily
correct to abort its simulation of E and reject this input as non-
halting.

Anyone that attempts to refute necessary truths is always necessarily
incorrect.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer