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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as
 non-halting V2
Date: Thu, 1 Aug 2024 06:56:31 -0500
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On 8/1/2024 2:49 AM, Mikko wrote:
> On 2024-07-31 17:28:38 +0000, olcott said:
> 
>> On 7/31/2024 2:36 AM, Mikko wrote:
>>> On 2024-07-16 18:18:07 +0000, olcott said:
>>>
>>>> On 7/16/2024 2:57 AM, Mikko wrote:
>>>>> On 2024-07-15 13:43:34 +0000, olcott said:
>>>>>
>>>>>> On 7/15/2024 3:17 AM, Mikko wrote:
>>>>>>> On 2024-07-14 14:50:47 +0000, olcott said:
>>>>>>>
>>>>>>>> On 7/14/2024 5:09 AM, Mikko wrote:
>>>>>>>>> On 2024-07-12 14:56:05 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> We stipulate that the only measure of a correct emulation is the
>>>>>>>>>> semantics of the x86 programming language.
>>>>>>>>>>
>>>>>>>>>> _DDD()
>>>>>>>>>> [00002163] 55         push ebp      ; housekeeping
>>>>>>>>>> [00002164] 8bec       mov ebp,esp   ; housekeeping
>>>>>>>>>> [00002166] 6863210000 push 00002163 ; push DDD
>>>>>>>>>> [0000216b] e853f4ffff call 000015c3 ; call HHH(DDD)
>>>>>>>>>> [00002170] 83c404     add esp,+04
>>>>>>>>>> [00002173] 5d         pop ebp
>>>>>>>>>> [00002174] c3         ret
>>>>>>>>>> Size in bytes:(0018) [00002174]
>>>>>>>>>>
>>>>>>>>>> When N steps of DDD are emulated by HHH according to the
>>>>>>>>>> semantics of the x86 language then N steps are emulated 
>>>>>>>>>> correctly.
>>>>>>>>>>
>>>>>>>>>> When we examine the infinite set of every HHH/DDD pair such that:
>>>>>>>>>> HHH₁ one step of DDD is correctly emulated by HHH.
>>>>>>>>>> HHH₂ two steps of DDD are correctly emulated by HHH.
>>>>>>>>>> HHH₃ three steps of DDD are correctly emulated by HHH.
>>>>>>>>>> ...
>>>>>>>>>> HHH∞ The emulation of DDD by HHH never stops running.
>>>>>>>>>>
>>>>>>>>>> The above specifies the infinite set of every HHH/DDD pair
>>>>>>>>>> where 1 to infinity steps of DDD are correctly emulated by HHH.
>>>>>>>>>
>>>>>>>>> You should use the indices here, too, e.g., "where 1 to 
>>>>>>>>> infinity steps of
>>>>>>>>> DDD₁ are correctly emulated by HHH₃" or whatever you mean.
>>>>>>>>>
>>>>>>>>
>>>>>>>> DDD is the exact same fixed constant finite string that
>>>>>>>> always calls HHH at the same fixed constant machine
>>>>>>>> address.
>>>>>>>
>>>>>>> If the function called by DDD is not part of the input then the 
>>>>>>> input does
>>>>>>> not specify a behaviour and the question whether DDD halts is 
>>>>>>> ill-posed.
>>>>>>>
>>>>>>
>>>>>> We don't care about whether HHH halts. We know that
>>>>>> HHH halts or fails to meet its design spec.
>>>>>>
>>>>>> We are only seeing if DDD correctly emulated by HHH
>>>>>> can can possibly reach its own final state.
>>>>>
>>>>> HHH does not see even that. It only sees whther that it does not 
>>>>> emulate
>>>>> DDD to its final state.
>>>>
>>>> No. HHH is not judging whether or not itself is a correct
>>>> emulator. The semantics of the x86 instructions that emulates
>>>> prove that its emulation is correct.
>>>
>>> Semantics of x86 language alone doesn't prove anything. Only a detailed
>>> comparison of the emulator code to the x86 semantics may prove that.
>>
>> A proof is any sequence of steps such that the conclusion
>> is a necessary consequence of its basis.
> 
> Only if every "step" is a sentence.
> 

Not at all.
My proof is the tautology that proves it is correct.

> Your traces are not such sequences.
> 
>> Proving that DDD correctly emulated by HHH matches the
>> infinite recursion behavior pattern.
>> (a) The semantics of the x86 language.
>> (b) the design of HHH provided below.
>> (c) The definition of infinite recursion provided below.
>>
>> *Infinite recursion behavior pattern*
>> An emulated sequence of instructions that has no conditional
>> branch instructions in this sequence is exactly repeated when
>> it calls the same function with the same parameters again.
>> As long as the called function can be determined to never
>> return this proves infinite recursion.
> 
> The recursive simulation does not satisfy the "no conditional branch"
> requirement so does not match the pattern.
> 

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     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

     H can abort its simulation of D and correctly report that D
     specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>

It freaking meets the above highlighted criteria.


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