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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: Wed, 24 Jul 2024 11:57:42 +0300
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On 2024-07-23 13:31:35 +0000, olcott said:

> On 7/23/2024 1:32 AM, 0 wrote:
>> On 2024-07-22 13:46:21 +0000, olcott said:
>> 
>>> On 7/22/2024 2:57 AM, Mikko wrote:
>>>> On 2024-07-21 13:34:40 +0000, olcott said:
>>>> 
>>>>> On 7/21/2024 4:34 AM, Mikko wrote:
>>>>>> On 2024-07-20 13:11:03 +0000, olcott said:
>>>>>> 
>>>>>>> On 7/20/2024 3:21 AM, Mikko wrote:
>>>>>>>> On 2024-07-19 14:08:24 +0000, olcott said:
>>>>>>>> 
>>>>>>>>> When we use your incorrect reasoning we would conclude
>>>>>>>>> that Infinite_Loop() is not an infinite loop because it
>>>>>>>>> only repeats until aborted and is aborted.
>>>>>>>> 
>>>>>>>> You and your HHH can reason or at least conclude correctly about
>>>>>>>> Infinite_Loop but not about DDD. Possibly because it prefers to
>>>>>>>> say "no", which is correct about Infinte_loop but not about DDD.
>>>>>>>> 
>>>>>>> 
>>>>>>> *Because this is true I don't understand how you are not simply lying*
>>>>>>> int main
>>>>>>> {
>>>>>>>    DDD();
>>>>>>> }
>>>>>>> 
>>>>>>> Calls HHH(DDD) that must abort the emulation of its input
>>>>>>> or {HHH, emulated DDD and executed DDD} never stop running.
>>>>>> 
>>>>>> You are the lying one.
>>>>>> 
>>>>>> If HHH(DDD) abrots its simulation and returns true it is correct as a
>>>>>> halt decider for DDD really halts.
>>>>>> 
>>>>> 
>>>>> (b) We know that a decider is not allowed to report on the behavior
>>>>> computation that itself is contained within.
>>>> 
>>>> No, we don't. There is no such prohibition.
>>>> 
>>> 
>>> Turing machines never take actual Turing machines as inputs.
>>> They only take finite strings as inputs and an actual executing
>>> Turing machine is not itself a finite string.
>> 
>> The definition of a Turing machine does not say that a Turing machine
>> is not a finite string. It is an abstract mathematical object without
>> a specification of its exact nature. It could be a set or a finite
>> string. Its exact nature is not relevant to the theory of computation,
>> which only cares about certain properties of Turing machines.
>> 
>>> Therefore It is not allowed to report on its own behavior.
>> 
>> Anyway, that does not follow. The theory of Turing machines does not
>> prohibit anything.
>> 
>>> Another different TM can take the TM description of this
>>> machine and thus accurately report on its actual behavior.
>> 
>> If a Turing machine can take a description of a TM as its input
>> or as a part of its input it can also take its own description.
>> Every Turing machine can be given its own description as input
>> but a Turing machine may interprete it as something else.
>> 
> In this case we have two x86utm machines that are identical
> except that DDD calls HHH and DDD does not call HHH1.

That DDD calls HHH and DDD does not call HHH1 is not a difference
between two unnamed turing machines.

-- 
Mikko