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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: DDD correctly emulated by HHH is correctly rejected as non-halting V2
Date: Tue, 16 Jul 2024 10:57:20 +0300
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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. But we can see more, in particuar that DDD() halts
if HHH(DDD) does.

Anyway, if the function DDD calls is not a part of the input then the
question whether DDD halts is not well-posed and can only be ansered
with a conditional.

-- 
Mikko