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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Defining a correct halt decider
Date: Thu, 5 Sep 2024 09:41:49 -0500
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On 9/5/2024 9:27 AM, joes wrote:
> Am Thu, 05 Sep 2024 08:39:14 -0500 schrieb olcott:
>> On 9/5/2024 2:39 AM, Mikko wrote:
>>> On 2024-09-03 13:17:56 +0000, olcott said:
>>>> On 9/3/2024 3:44 AM, Mikko wrote:
>>>>> On 2024-09-02 16:06:11 +0000, olcott said:
>>>>>
>>>>>> A correct halt decider is a Turing machine T with one accept state
>>>>>> and one reject state such that:
>>>>>> If T is executed with initial tape contents equal to an encoding of
>>>>>> Turing machine X and its initial tape contents Y, and execution of a
>>>>>> real machine X with initial tape contents Y eventually halts, the
>>>>>> execution of T eventually ends up in the accept state and then
>>>>>> stops.
>>>>>> If T is executed with initial tape contents equal to an encoding of
>>>>>> Turing machine X and its initial tape contents Y, and execution of a
>>>>>> real machine X with initial tape contents Y does not eventually
>>>>>> halt, the execution of T eventually ends up in the reject state and
>>>>>> then stops.
>>>>>
>>>>> Your "definition" fails to specify "encoding". There is no standard
>>>>> encoding of Turing machines and tape contents.
>>>>
>>>> That is why I made the isomorphic x86utm system.
>>>> By failing to have such a concrete system all kinds of false
>>>> assumptions cannot be refuted.
>>> If it were isnomorphic the same false assumtipns would apply to both.
>>
>> They do yet I cannot provide every single details of the source-code of
>> the Turing machine because these details would be too overwhelming.
> 
>> So instead every author makes a false assumption that is simply believed
>> to be true with no sufficient basis to show that it isn't true.
> What is that assumption?
> 
>>>> The behavior of DDD emulated by HHH** <is> different than the behavior
>>>> of the directly executed DDD** **according to the semantics of the x86
>>>> language
>>> The halting problem is not about a string but about a behaviour.
>>
>> Is is about the behavior that this string specifies.
> Namely, that DDD halts.
> 
>> HHH computes the mapping from its input finite string to the behavior
>> that this finite string specifies on the basis of DDD emulated by HHH.
> The wrinkle being that it is selfreferential. We are only interested
> in the case where the DDD that calls an aborting HHH is simulated
> by that same HHH.
> 
>> DDD emulated by HHH cannot possibly reach its final halt state and on
>> this basis alone HHH is correct to reject DDD and report non-halting.
> HHH cannot simulate something that calls itself; yet it halts.
> 
>> That no one bothered to notice that the behavior of an input DDD to a
>> simulating termination analyzer HHH can be different than the behavior
>> of a directly executed DDD when there is a pathological relationship
>> between HHH and DDD IS NOT MY MISTAKE.
> That is exactly your mistake, that you believe the simulation of a
> different program somehow has the same behaviour.

DDD emulated by HHH never reaches it final halt state.
It looks like I have to repeat this 10,000 times before
anyone ever notices that I said it at least once.

_DDD()
[00002172] 55         push ebp      ; housekeeping
[00002173] 8bec       mov ebp,esp   ; housekeeping
[00002175] 6872210000 push 00002172 ; push DDD
[0000217a] e853f4ffff call 000015d2 ; call HHH(DDD)
[0000217f] 83c404     add esp,+04
[00002182] 5d         pop ebp
[00002183] c3         ret
Size in bytes:(0018) [00002183]

Show the details of how DDD emulated by HHH
reaches its own machine address 0000217f.

00002172, 00002173, 00002175, 0000217a calls HHH(DDD)
then
00002172, 00002173, 00002175, 0000217a calls HHH(DDD)...


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