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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory
Subject: Re: Defining a correct halt decider
Date: Fri, 6 Sep 2024 11:11:13 +0200
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Op 05.sep.2024 om 16:41 schreef olcott:
> 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.
Problems in processing English? I think everybody agrees that HHH fails 
to reach the final halt state.
There is a final halt state that can be reached by the direct execution, 
by the unmodified world class simulator and even by HHH1. But HHH fails 
to reach this final halt state.
How many times must it be repeated before olcott reads it once?
HHH cannot possibly simulate itself correctly up to the end.