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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 --mistake--
Date: Fri, 15 Mar 2024 22:14:08 -0500
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On 3/15/2024 6:26 PM, Richard Damon wrote:
> On 3/15/24 3:41 PM, olcott wrote:
>> On 3/15/2024 5:10 PM, Richard Damon wrote:
>>> On 3/15/24 2:13 PM, olcott wrote:
>>>> On 3/15/2024 3:27 PM, Richard Damon wrote:
>>>>> On 3/15/24 12:38 PM, olcott wrote:
>>>>>> On 3/15/2024 2:30 PM, Richard Damon wrote:
>>>>>>> On 3/15/24 12:14 PM, olcott wrote:
>>>>>>>> On 3/15/2024 2:06 PM, Richard Damon wrote:
>>>>>>>>> On 3/15/24 11:39 AM, olcott wrote:
>>>>>>>>>> On 3/15/2024 1:38 PM, immibis wrote:
>>>>>>>>>>> On 15/03/24 18:52, olcott wrote:
>>>>>>>>>>>> On 3/15/2024 12:36 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/15/24 9:20 AM, 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).
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Except that D calling H(D,D) does NOT prove the required 
>>>>>>>>>>>>> (a), since the simulated D WILL stop running because *ITS* 
>>>>>>>>>>>>> H will abort *ITS* simulation and returm 0 so that 
>>>>>>>>>>>>> simulated D will halt.
>>>>>>>>>>>> You keep saying that H(D,D) never really needs to abort the
>>>>>>>>>>>> simulation of its input because after H(D,D) has aborted the
>>>>>>>>>>>> simulation of this input it no longer needs to be aborted.
>>>>>>>>>>>>
>>>>>>>>>>> You keep thinking there is more than one H(D,D) and then when 
>>>>>>>>>>> it's convenient for you you think there is only one H(D,D). 
>>>>>>>>>>> Why is that?
>>>>>>>>>>
>>>>>>>>>> The first H(D,D) to see that the abort criteria has been met
>>>>>>>>>> (the outermost one) must abort the simulation of its input or
>>>>>>>>>> none of them ever abort.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> But since it does, which is your definition of H, the others 
>>>>>>>>
>>>>>>>> never begin to be simulated.
>>>>>>>
>>>>>>> But D(D) started to be simulated, and we can know what D(D) 
>>>>>>> actually does, which includes it using its version of H.
>>>>>>>
>>>>>>
>>>>>> We cannot reference the behavior of what D(D) does after H(D,D)
>>>>>> has already aborted the simulation of its input at the point
>>>>>> in time before H(D,D) aborts its input as any criterion measure
>>>>>> for this H(D,D).
>>>>>>
>>>>>
>>>>> WHy not?
>>>>>
>>>>> That is what Correct Simulation refers to.
>>>>>
>>>>> I guess you are just admiting to being a LIAR (or stupid).
>>>>
>>>> *I am not a liar or stupid and you admitted your mistake*
>>>> *I am not a liar or stupid and you admitted your mistake*
>>>> *I am not a liar or stupid and you admitted your mistake*
>>>> *I am not a liar or stupid and you admitted your mistake*
>>>
>>> So, do you admit that the definition of a "Correct Simulation" for 
>>> the purposes of that criteria are the complete not-aborted simulation 
>>> done by possibly some other simulator?
>>>
>>
>> (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
>>
>> Not at all the words don't say anything like that.
>> "H correctly simulates its input D until"
>> specifically means a partial simulation.
>>
> 
> Means H uses a partial simulation to make its decision.
> 

Finally you get this.

> The correctness of the decision is measured by the full simulation, even 
> past where H simulated. Thus, is based on things H might not know.
> 

No. the correctness of the decision is essentially anchored
in something like mathematical induction that correctly
predicts that complete simulation would never end.

I would estimate that an actual proof fully anchored in actual
mathematical induction can be derived. I do remember from my
independent studies course on proof of program correctness that
this does typically anchor in actual mathematical induction.

I still have two textbooks on this.

> You don't seem to understand the meaning of CORRECT.
> 
> I guess you are just showing you think it is ok to LIE to make it look 
> like you have done something.
> 

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