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From: =?UTF-8?B?QW5kcsOpIEcuIElzYWFr?= <agisaak@gm.invalid>
Newsgroups: comp.theory
Subject: Re: Correcting the definition of the halting problem --- Computable
 functions
Date: Mon, 24 Mar 2025 18:00:26 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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On 2025-03-24 17:42, olcott wrote:
> On 3/24/2025 6:05 PM, André G. Isaak wrote:
>> On 2025-03-24 17:04, olcott wrote:


>>> _III()
>>> [00002172] 55         push ebp      ; housekeeping
>>> [00002173] 8bec       mov  ebp,esp  ; housekeeping
>>> [00002175] 6872210000 push 00002172 ; push III
>>> [0000217a] e853f4ffff call 000015d2 ; call EEE(III)
>>> [0000217f] 83c404     add  esp,+04
>>> [00002182] 5d         pop  ebp
>>> [00002183] c3         ret
>>> Size in bytes:(0018) [00002183]
>>>
>>> When III is emulated by pure emulator EEE for any finite
>>> number of steps of emulation according to the semantics
>>> of the x86 language it never reaches its own "ret"
>>> instruction final halt state THUS DOES NOT HALT.
>>>
>>> When III is directly executed calls an EEE instance
>>> that only emulates finite number of steps then this
>>> directly executed III always reaches its own "ret"
>>> instruction final halt state THUS HALTS.
>>
>> And that has what, exactly, to do with the post you are allegedly 
>> responding to?
>>
>> André
>>
> 
> 
> THE INPUT FINITE STRING DOES SPECIFY RECURSIVE EMULATION.
> 
> The behavior specified by the finite string input to a
> computable function implemented on a model of computation
> 
> does differ from the direct execution of this same finite
> string because the direct execution avoids the pathological
> self-reference that causes the recursive emulation.
> 
> THE INPUT FINITE STRING DOES SPECIFY RECURSIVE EMULATION.

In the post you were responding to I pointed out that computable 
functions are mathematical objects. The above copypasta doesn't address 
this.

I pointed out that the domain of a computable function needn't be a 
string. The above copypasta doesn't address this.

I pointed out that there is no bijection natural numbers and strings, 
but rather a one-to-many relation. The above copypasta doesn't address this.

I pointed out that the exact same sort of one-to-many relation exists 
between computations and strings. The above copypasta doesn't address this.

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