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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Is Richard a Liar?
Date: Fri, 17 May 2024 12:28:14 +0300
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On 2024-05-16 14:37:59 +0000, olcott said:

> 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.

In the usual language of regular expressions the wildcard
metacharecter is point "." and the metacaracters "*", "+"
denote repetition, "+" at least once.

That a "wildcard" is a well known word is one of the reasons
why the term should not be used when the same meaning is not
applicable.

Another reason is that one should never use a word where it
does not affect the meaning of the containing expression. As
"⊢*" means 'a sequence of moves' you shold not use more words
to express its meaning.

Yeat another reason is that when one borrows a notation one
should also borrow the terms used in discussion of the notation
unles they conflict with terms borrowed from elsewhere.

>>>> 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.

No, it is not. A machine where several parts are executed at the same
time is not a Turing machine. If a part of a Turing machine never
stops it execution it perevents all execution of other parts.

-- 
Mikko