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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Every D correctly simulated by H cannot possibly reach its own
 line 06 and halt
Date: Tue, 21 May 2024 21:05:51 -0500
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On 5/21/2024 8:46 PM, Richard Damon wrote:
> On 5/21/24 10:22 AM, olcott wrote:
>> On 5/21/2024 7:03 AM, Richard Damon wrote:
>>> On 5/21/24 1:18 AM, olcott wrote:
>>>> On 5/20/2024 9:39 PM, Richard Damon wrote:
>>>>> On 5/20/24 10:25 PM, olcott wrote:
>>>>>> On 5/20/2024 7:57 PM, Richard Damon wrote:
>>>>>>> On 5/20/24 2:03 PM, olcott wrote:
>>>>>>>> On 5/20/2024 6:24 AM, Richard Damon wrote:
>>>>>>>>> On 5/19/24 11:22 PM, olcott wrote:
>>>>>>>>>> On 5/19/2024 10:11 PM, Richard Damon wrote:
>>>>>>>>>>> On 5/19/24 10:52 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.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> OK, good.
>>>>>>>>>>>
>>>>>>>>>>> Right, so it doesn't matter what any other D does, it matters 
>>>>>>>>>>> what THIS D does, and this D calls aths H.
>>>>>>>>>>>
>>>>>>>>>>> Remember, you reinstated the Computation model by enforcing 
>>>>>>>>>>> Pure Functions.
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> <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.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> That is off-topic for this post.
>>>>>>>>>>>> All that we need know is that no D simulated by any H
>>>>>>>>>>>> ever reaches its own line 06 and halts.
>>>>>>>>>>>
>>>>>>>>>>> Nope. Make a claim, you need to prove it.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> *In other different post not this one*
>>>>>>>>>>
>>>>>>>>>> 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.
>>>>>>>>>
>>>>>>>>> But you can't PRECISELY define the category, or what you want 
>>>>>>>>> to reason about, so your logic is worthless as it is baseless.
>>>>>>>>>
>>>>>>>>
>>>>>>>> *POINT TO ANY ACTUAL MISTAKE OR AMBIGUITY WITH THIS VERSION*
>>>>>>>>
>>>>>>>> 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.
>>>>>>>>
>>>>>>>
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