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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Is Richard a Liar?
Date: Thu, 16 May 2024 09:37:59 -0500
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On 5/16/2024 5:15 AM, Mikko wrote:
> On 2024-05-15 15:03:20 +0000, olcott said:
> 
>> On 5/15/2024 3:04 AM, Mikko wrote:
>>> On 2024-05-14 14:21:10 +0000, olcott said:
>>>
>>>> On 5/14/2024 4:44 AM, Mikko wrote:
>>>>> On 2024-05-12 15:58:02 +0000, olcott said:
>>>>>
>>>>>> On 5/12/2024 10:21 AM, Mikko wrote:
>>>>>>> On 2024-05-12 11:34:17 +0000, Richard Damon said:
>>>>>>>
>>>>>>>> On 5/12/24 5:19 AM, Mikko wrote:
>>>>>>>>> On 2024-05-11 16:26:30 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> I am working on providing an academic quality definition of this
>>>>>>>>>> term.
>>>>>>>>>
>>>>>>>>> The definition in Wikipedia is good enough.
>>>>>>>>>
>>>>>>>>
>>>>>>>> I think he means, he is working on a definition that redefines 
>>>>>>>> the field to allow him to claim what he wants.
>>>>>>>
>>>>>>> Here one can claim whatever one wants anysay.
>>>>>>> In if one wants to present ones claims on some significant forum 
>>>>>>> then
>>>>>>> it is better to stick to usual definitions as much as possible.
>>>>>>>
>>>>>>>> Sort of like his new definition of H as an "unconventional" 
>>>>>>>> machine that some how both returns an answer but also keeps on 
>>>>>>>> running.
>>>>>>>
>>>>>>> There are systems where that is possible but unsolvable problems are
>>>>>>> unsolvable even in those systems.
>>>>>>>
>>>>>>
>>>>>> When Ĥ is applied to ⟨Ĥ⟩
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> This notation does not work with machines that can, or have parts
>>>>> that can, return a value without (or before) termination.
>>>>>
>>>>
>>>> ⊢* specifies a wildcard set of state transitions that could
>>>> include a transition to a non-final state embedded_H.qn.
>>>
>>> The term "wildcard" is usually not used in this context. And the word
>>> "set" is not sufficiently specific, so "sequence" should be used 
>>> instead.
>>>
>>
>> Yes that is better.
>> ⊢* specifies a wildcard sequence of state transitions
> 
> That still has the problem that "wildcard" has no well known meaning
> that could be applicable in that context.
> 
>> *Here is how Linz says it*
>> The Linz term “move” means a state transition and its corresponding
>> tape head action {move_left, move_right, read, write}.
>> ⊢* indicates an arbitrary number of moves.
> 
> I.e., a sequence of moves.
> 

Not as easy for software engineers.
Wildcard as * was one of the first things that I learned.
It is well known in the field of regular expressions.

>>> Anyway, the language cannot handle a situation where one part of a
>>> machine gives its result to another parts and then both continue their
>>> execution.
>>
>> The language of Turing machine descriptions certainly can handle
>> TM's that do not halt. It can also handle transitioning through
>> a specific state to another state.
> 
> Yes, but a machine were one part of a machine gives its result to
> aonter part and then both continue their exection is not a Truing
> machine. 

Sure it is. A Turing machine that transitions through a specific state
and never stops running IS A TURING MACHINE. The prior state-of-the-art
is that both YES and NO are the wrong answer from TM H regarding the
behavior of input D. I provide a counter-example that PROVES that YES
is the correct answer.

> Consequently, when you introduced that possibility were
> not discussing Turing machines. A language decined for Turing
> mahihes is not sufficient for non-Turing machines.
> 

*A Turing machine that transitions through a specific*
*state and never stops running IS A TURING MACHINE*
*Every specific type of Turing Machine <is> a Turing Machine*

>> This specific state can encode a halt status value. New ideas are
>> hard because there is no standard boiler-plate that can be applied
>> to them.
> 
> The specification of the halt decider requires that the halt status
> value is indicated by the final state.
> 

Going from both YES and NO are the wrong answer from H about D
to YES is the correct answer about D is an incremental improvement.

The least that we can say about this is that H KNOWS the correct
answer yet cannot SAY the correct answer in the conventional way.

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