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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 --Categorically
 Exhaustive Reasoning--
Date: Sat, 16 Mar 2024 10:23:54 -0500
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On 3/16/2024 12:22 AM, Richard Damon wrote:
> On 3/15/24 10:00 PM, olcott wrote:
>> On 3/15/2024 11:52 PM, Richard Damon wrote:
>>> On 3/15/24 8:41 PM, olcott wrote:
>>>> On 3/15/2024 10:11 PM, Richard Damon wrote:
>>>>> On 3/15/24 8:00 PM, olcott wrote:
>>>>>> On 3/15/2024 9:47 PM, Richard Damon wrote:
>>>>>>> On 3/15/24 7:18 PM, olcott wrote:
>>>>>>>> On 3/15/2024 8:22 PM, Richard Damon wrote:
>>>>>>>>> On 3/15/24 5:49 PM, olcott wrote:
>>>>>>>>>> On 3/15/2024 6:37 PM, Mike Terry wrote:
>>>>>>>>>>> On 15/03/2024 18:45, immibis wrote:
>>>>>>>>>>>> On 15/03/24 19:39, 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.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> that's wrong. They all abort, so if we prevent the first one 
>>>>>>>>>>>> from aborting, the second one will abort. If we prevent the 
>>>>>>>>>>>> first and second ones from aborting, the third one will abort. 
>>>>>>>>>>>
>>>>>>>>>>> Correct - but PO has the wrong understanding of "prevent".
>>>>>>>>>>>
>>>>>>>>>>> Correct understanding:  We're discussing a (putative) HD H 
>>>>>>>>>>> examining an input (P,I) representing some /fixed/ 
>>>>>>>>>>> computation. When we talk about "preventing" H from doing 
>>>>>>>>>>> xxxxx (such as aborting a simulation) we mean how an amended 
>>>>>>>>>>> version H2 (like H but without xxxxx) behaves in examining 
>>>>>>>>>>> that /same input/ (P,I).
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> *It can be construed that way, yet that is not it*
>>>>>>>>>> In software engineering the above is simply a pair of distinct
>>>>>>>>>> execution paths based on a conditional test within the same 
>>>>>>>>>> program.
>>>>>>>>>> In both cases D is simply a fixed constant string of 
>>>>>>>>>> machine-code bytes.
>>>>>>>>>
>>>>>>>>> Right D is a FIXED constant string, and thus the meaning 
>>>>>>>>> doesn't change if we hypothsize about changing an H.
>>>>>>>>>
>>>>>>>> It always calls whatever H is at the fixed machine address
>>>>>>>> that is encoded within D.
>>>>>>>
>>>>>>> In other words, it has NOTHING to do with Turing Machines, and 
>>>>>>> thus has NO application to the Linz proof, and you are admitting 
>>>>>>> you are LYING about it having application.
>>>>>>>
>>>>>>> As D isn't a "Computation" as it takes a "hidden input", namely 
>>>>>>> thely the contents of them memory now called "H". (It isn't PART 
>>>>>>> OF D, and isn't a declared parameter to D, so it is a "Hidden Input"
>>>>>>>
>>>>>>
>>>>>> I told you that you will not have the basis (prerequisite knowledge)
>>>>>> to see how this is isomorphic to H ⟨Ĥ⟩ ⟨Ĥ⟩ until after you see how
>>>>>> H(D,D) does correctly determine that it must abort its simulation.
>>>>>>
>>>>>>>>
>>>>>>>> This means that it DOES call H(D,D) in recursive simulation and
>>>>>>>> DOES NOT call H1(D,D) in recursive simulation.
>>>>>>>>
>>>>>>>
>>>>>>> And means you have been LYING that it has ANYTHING to do with the 
>>>>>>> HALTING PROBLEM
>>>>>>>
>>>>>>>> Thus H(D,D) must account for this difference and H1(D,D) can
>>>>>>>> ignore this difference.
>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> When we use categorically exhaustive reasoning instead of locking
>>>>>>>>>> ourselves into the pathological thinking of Richard where H tries
>>>>>>>>>> to second guess itself such that anything that H(D,D) does can 
>>>>>>>>>> somehow
>>>>>>>>>> be construed as incorrect...
>>>>>>>>>
>>>>>>>>> Sounds like buzzwords.
>>>>>>>>>
>>>>>>>>> H doesn't try to second guess, H does what H does. PERIOD. That 
>>>>>>>>> is all it can do.
>>>>>>>>>
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