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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 19:06:18 -0500
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On 3/16/2024 6:54 PM, Richard Damon wrote:
> On 3/16/24 11:57 AM, olcott wrote:
>> On 3/16/2024 12:33 PM, immibis wrote:
>>> On 16/03/24 18:04, olcott wrote:
>>>> On 3/16/2024 11:53 AM, Richard Damon wrote:
>>>>> On 3/16/24 8:23 AM, olcott wrote:
>>>>>> 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, 
========== REMAINDER OF ARTICLE TRUNCATED ==========