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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 23:23:27 -0500
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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.

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