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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 14:37:23 -0400
Organization: i2pn2 (i2pn.org)
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On 3/29/25 11:25 AM, olcott wrote:
> On 3/29/2025 4:27 AM, joes wrote:
>> Am Fri, 28 Mar 2025 14:38:35 -0500 schrieb olcott:
>>> On 3/28/2025 2:20 PM, dbush wrote:
>>>> On 3/28/2025 3:15 PM, olcott wrote:
>>>>> On 3/28/2025 4:33 AM, Fred. Zwarts wrote:
>>>>>> Op 28.mrt.2025 om 02:21 schreef olcott:
>>>>>>> On 3/27/2025 8:09 PM, dbush wrote:
>>>>>>>> On 3/27/2025 9:07 PM, olcott wrote:
>>>>>>>>> On 3/27/2025 7:38 PM, dbush wrote:
>>>>>>>>>> On 3/27/2025 8:34 PM, olcott wrote:
>>
>>>>>>> I did not say that no TM can ever report on behavior that matches
>>>>>>> the behavior of a directly executing TM.
> 
>> Why can't HHH do it? Explain what pathology is and what it does.
>>
>>>>>>> No TM can every directly see the behavior of the direct execution of
>>>>>>> any other TM because no TM can take a directly executing TM as an
>>>>>>> input.
> 
>> Ridiculous strawman, nobody said that. Are you saying that nothing at
>> all can be computed about TMs?
>>
> 
> If HHH must report on the direct execution of DDD
> then it must see the behavior of the direct
> execution of DDD and this is always impossible
> for every pair of TMs.
> 
>>>>>> So we agree that the answer for:
>>>>>> 'Is there an algorithm that can determine for all possible inputs
>>>>>> whether the input specifies a program that (according to the
>>>>>> semantics of the machine language) halts when directly executed?'
>>>>>> is 'no'. Correct?
>>>>>
>>>>> In the same way: Is there an algorithm that correctly determines the
>>>>> square root of a box of rocks?
> 
>> Can you just say yes or no for once?
>>
> The inability to determine whether or not
> this sentence: "What time is it?" is true
> or false is not any instance of undecidability.
> 
> The inability of any TM to report on the behavior
> of the direct execution of any other TM is also
> not any instance of undecidability.
> 
>>>> In other words, you're saying that there's a TM/input where the
>>>> question of whether or not it halts when executed directly has no
>>>> correct yes or no answer.
>>>> Show it.
>>>>
>>> I proved it many times and because you are a Troll you ignored the proof
>>> that by definition no TM can take an executing TM as its input, thus
>>> cannot possibly report on something that it does not see.
> 
>> Where is the proof that some TM has no definite halting status?
>>
> 
> No TM can ever report on the behavior of any directly
> executed TM because no TM has any access to this behavior.

Sure it does. That is what a UTM is.

> 
>>>> Failure to do so in your next message is your on-the-record admission
>>>> that the above question is valid.
>>>
>>> When include ALL of the relevant details to the question it becomes:
>>> What Boolean value can decider H correctly return when input D is able
>>> to do the opposite of whatever value that H returns?
> 
>> And the answer is none, ergo the assumption that an H exists is wrong.
>>
> 
> Likewise by the same reasoning we can prove that some
> questions have no correct answer by allowing incorrect
> questions.

yes, YOUR question is the incorrect one.

The Halting Problem asks a correct one: "Does the TM described by the 
input Halt (when run)?"

That has an answer, just not the one that your decider gives.

> 
>>> We can reject this question entirely when we discard its false
>>> assumption. D is unable to do the opposite of whatever value that H
>>> returns when H is a simulating halt decider.
> 
>> Oh. That's a rather unorthodox resolution. How do you show that D
>> is impossible.
>>
> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> The contradictory part is unreachable code to
> DD correctly emulated by HHH.
> 

But HHH doesn't correectly emulate DD, so you statement is just a LIE.

Note, to actually do this, you need to include in the "input" DD, the 
full code of the sub-program HHH, or you are just making a category 
error in your question.