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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Proof that H(D,D) meets its abort criteria
Date: Fri, 15 Mar 2024 12:23:18 -0500
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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.

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