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From: immibis <news@immibis.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Proof that H(D,D) meets its abort criteria
Date: Fri, 15 Mar 2024 19:37:51 +0100
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On 15/03/24 18:23, olcott wrote:
> On 3/15/2024 12:07 PM, immibis wrote:
>> On 15/03/24 17:20, olcott wrote:
>>> Best selling author of Theory of Computation textbooks:
>>> *Introduction To The Theory Of Computation 3RD, by sipser*
>>> https://www.amazon.com/Introduction-Theory-Computation-Sipser/dp/8131525295/
>>>
>>> Date 10/13/2022 11:29:23 AM
>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is correct*
>>> (He has neither reviewed nor agreed to anything else in this paper)
>>> (a) 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
>>> (b) H can abort its simulation of D and correctly report that D 
>>> specifies a non-halting sequence of configurations.
>>>
>>> *When we apply the abort criteria* (elaborated above)
>>> Will you halt if you never abort your simulation?
>>> *Then H(D,D) is proven to meet this criteria*
>>>
>>> *Proof that H(D,D) meets its abort criteria*
>>>
>>> int D(int (*x)())
>>> {
>>>    int Halt_Status = H(x, x);
>>>    if (Halt_Status)
>>>      HERE: goto HERE;
>>>    return Halt_Status;
>>> }
>>>
>>> int main()
>>> {
>>>    Output("Input_Halts = ", H(D,D));
>>> }
>>>
>>>   machine   stack     stack     machine    assembly
>>>   address   address   data      code       language
>>>   ========  ========  ========  =========  =============
>>> [00001d22][00102fc9][00000000] 55         push ebp      ; begin main()
>>> [00001d23][00102fc9][00000000] 8bec       mov ebp,esp
>>> [00001d25][00102fc5][00001cf2] 68f21c0000 push 00001cf2 ; push DD
>>> [00001d2a][00102fc1][00001cf2] 68f21c0000 push 00001cf2 ; push D
>>> [00001d2f][00102fbd][00001d34] e8eef7ffff call 00001522 ; call H(D,D)
>>>
>>> H: Begin Simulation   Execution Trace Stored at:113075
>>> Address_of_H:1522
>>> [00001cf2][00113061][00113065] 55         push ebp       ; enter D(D)
>>> [00001cf3][00113061][00113065] 8bec       mov ebp,esp
>>> [00001cf5][0011305d][00103031] 51         push ecx
>>> [00001cf6][0011305d][00103031] 8b4508     mov eax,[ebp+08]
>>> [00001cf9][00113059][00001cf2] 50         push eax       ; push D
>>> [00001cfa][00113059][00001cf2] 8b4d08     mov ecx,[ebp+08]
>>> [00001cfd][00113055][00001cf2] 51         push ecx       ; push D
>>> [00001cfe][00113051][00001d03] e81ff8ffff call 00001522  ; call H(D,D)
>>> H: Recursive Simulation Detected Simulation Stopped
>>>                            H(D,D) returns 0 to main()
>>>
>>> *That was proof that H(D,D) meets its abort criteria*
>>> H(D,D) correctly determines that itself is being called with its same 
>>> inputs and there are no conditional branch instructions between the 
>>> invocation of D(D) and its call to H(D,D).
>>>
>>>
>>
>> There are conditional branch instructions inside H(D,D). This is 
>> obvious. Why do you keep lying?
> 
> (a) 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
> 
> It is true that D(D) would never stop running unless the
> outermost H(D,D) aborts its simulation thus meeting the
> above criteria.
> 
It is true that D(D) would never stop running unless the SIMULATED 
H(D,D) aborts its simulation or does not run a simulation or the 
simulation halts.