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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: Sat, 16 Mar 2024 10:28:05 -0500
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On 3/15/2024 11:43 PM, Richard Damon wrote:
> On 3/15/24 9:23 PM, olcott wrote:
>> On 3/15/2024 10:55 PM, immibis wrote:
>>> On 16/03/24 04:14, olcott wrote:
>>>> 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.
>>>
>>> The correctness of the decision is anchored in whether D(D) halts or 
>>> not.
>>
>> A termination analyzer must have some way to predicate this.
>> H(D,D) can only predict what it actually sees and H(D,D)
>> sees that it must abort the simulation of its input.
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