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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D correctly simulated by H cannot possible reach its own
 line 06 and halt
Date: Mon, 20 May 2024 13:01:23 -0500
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On 5/20/2024 6:24 AM, Richard Damon wrote:
> On 5/19/24 11:32 PM, olcott wrote:
>> On 5/19/2024 10:24 PM, Richard Damon wrote:
>>> On 5/19/24 11:09 PM, olcott wrote:
>>>> On 5/19/2024 8:10 PM, Richard Damon wrote:
>>>>> On 5/19/24 8:06 PM, olcott wrote:
>>>>>> On 5/1/2024 7:10 PM, Richard Damon wrote:
>>>>>>
>>>>>> typedef int (*ptr)();  // ptr is pointer to int function
>>>>>> 00 int H(ptr p, ptr i);
>>>>>> 01 int D(ptr p)
>>>>>> 02 {
>>>>>> 03   int Halt_Status = H(p, p);
>>>>>> 04   if (Halt_Status)
>>>>>> 05     HERE: goto HERE;
>>>>>> 06   return Halt_Status;
>>>>>> 07 }
>>>>>> 08
>>>>>> 09 int main()
>>>>>> 10 {
>>>>>> 11   H(D,D);
>>>>>> 12   return 0;
>>>>>> 13 }
>>>>>>
>>>>>> In the above case a simulator is an x86 emulator that correctly 
>>>>>> emulates at least one of the x86 instructions of D in the order 
>>>>>> specified by the x86 instructions of D.
>>>>>>
>>>>>> This may include correctly emulating the x86 instructions of H in 
>>>>>> the order specified by the x86 instructions of H thus calling 
>>>>>> H(D,D) in recursive simulation.
>>>>>>
>>>>>> For every H/D pair of the above template D correctly simulated by
>>>>>> *pure function* H cannot possibly reach its own final state at
>>>>>> line 06 and halt.
>>>>>>
>>>>>
>>>>> Ok, so adding that H is a pure function, that means that since your 
>>>>> outer H(D,D) is going to return 0, all logic must be compatible 
>>>>> with the fact that EVERY call to H(D,D) will also eventually return 0.
>>>>>
>>>>>
>>>>> Remember also, THIS D is defined to call THIS H, that does exactly 
>>>>> the same as the H that is deciding it.
>>>>>
>>>>>>
>>>>>> <snip so that Message ID links to whole message>
>>>>>> We can use my unique time/date stamp as an alternative.
>>>>>>
>>>>>>> Remember, YOU are the one saying you are needing to change the 
>>>>>>> definition from the classical theory, where we have things well 
>>>>>>> defined.
>>>>>>>
>>>>>>> YOU have decider that H is just whatever C code you want to write 
>>>>>>> for it, and D is the input proved. (which doesn't actually match 
>>>>>>> the Linz or Sipser proof, but fairly close).
>>>>>>>
>>>>>>> With THAT set of definitions we have a lot of options that break 
>>>>>>> your incorrectly assumed results.
>>>>>>>
>>>>>>> The first method has been discussed here by Flibble. While the 
>>>>>>> final answer he got to doesn't fit the requirements, the first 
>>>>>>> part of the method DOES show that it is possible for an H to 
>>>>>>> simulate to past line 3.
>>>>>>>
>>>>>>> THe basic idea is that if H(M,d) finds that its simulation of 
>>>>>>> M(d) get to a call to H(M,d) then rather that your idea of just 
>>>>>>> saying it will get stuck and declair the input invalid, since 
>>>>>>> there ARE a number of possible inputs that there is a "correct" 
>>>>>>> answer that H can give to 
>>>>>>
>>>>>> That D is calling H does not prove recursive simulation.
>>>>>> That D is calling H with its same parameters does seem
>>>>>> to prove non-halting recursive simulation.
>>>>>
>>>>> Nope. Try to actuall PROVE it.
>>>>
>>>> I am using categorically exhaustive reasoning that can work
>>>> through every possibility that can possibly exist in a feasible
>>>> amount of time as long as the category is very very narrow.
>>>
>>> What "Category", we have a specified H and an SPECIFIED D.
>>>
>>> The question is not, can H simulate D to the end, the question is 
>>> does D halt.
>>>
>>
>> *The subject is in the subject line you diverged, please try again*
>> *The subject is in the subject line you diverged, please try again*
>> *The subject is in the subject line you diverged, please try again*
>>
> 
> And since YOU brought up the diversion, I just asked you to define it.
> 

typedef int (*ptr)();  // ptr is pointer to int function
00 int H(ptr p, ptr i);
01 int D(ptr p)
02 {
03   int Halt_Status = H(p, p);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 int main()
10 {
11   H(D,D);
12   return 0;
13 }

In the above case a simulator is an x86 emulator that correctly emulates 
at least one of the x86 instructions of D in the order specified by the 
x86 instructions of D.

This may include correctly emulating the x86 instructions of H in the 
order specified by the x86 instructions of H thus calling H(D,D) in 
recursive simulation.

Execution Trace
Line 11: main() invokes H(D,D);

keeps repeating (unless aborted)
Line 01:
Line 02:
Line 03: simulated D(D) invokes simulated H(D,D) that simulates D(D)

Simulation invariant:
D correctly simulated by H cannot possibly reach past its own line 03.

For every H/D pair of the above template D correctly simulated by pure 
function (thus computable function) H cannot possibly reach its own 
final state at line 06 and halt.

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