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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Richard is proven to be incorrect on a key point
Date: Sat, 18 May 2024 09:53:06 -0500
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On 5/18/2024 5:38 AM, Mikko wrote:
> On 2024-05-18 01:07:17 +0000, Richard Damon said:
> 
>> On 5/17/24 12:07 PM, olcott wrote:
>>> On 5/17/2024 4:28 AM, Mikko wrote:
>>>> 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 is not the term used when computer science students are taught
>>> how to find files matching a pattern. I know a lot about deterministic
>>> finite automatons having two issued patents on them.
>>
>> Nope, that IS the definition of REGULAR EXPRESSION, it isn't the 
>> definitoin of GLOBBING like is done at the command line.
>>
>> Look at https://en.wikipedia.org/wiki/Regular_expression
>>
>>
>> The asterisk indicates zero or more occurrences of the preceding 
>> element. For example, ab*c matches "ac", "abc", "abbc", "abbbc", and 
>> so on.
>>
>>>
>>> I know a lot about regular expressions because I used regular
>>> expressions in the AWK programming language to search a massive
>>> code-base of millions of lines to analyze the system that required
>>> maintenance.
>>>
>>>> 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.
>>>>
>>>
>>> It does include zero or more state transitions in a sequence of state
>>> transitions. Linz calls this moves to also include tape head actions.
>>>
>>>> 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.
>>>>
>>>
>>> Several of my reviewers took a very long time to understand that
>>> the Linz proof refers to Turing machine description templates and
>>> not a single Turing machine. We had to go over this exact same
>>> thing many hundreds of times.
>>
>> Nope, Linz CLEARLY refers to H in the singular as a single machine.
>>
>> The diagram is a requirements statement that H must meet, but H is not 
>> "at once" all machines that meet that requirement.
>>
>>>
>>>> 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.
>>>>
>>>
>>> It might be best if I simply directly quote Linz and then explain his
>>> words in terms that software engineers can understand.
>>
>> Try it.
>>
>>>
>>>>>>>> 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.
>>>
>>> (1)--->(2)--->(3) is a DFA that transitions through its state (2).
>>> A TM can transition through a specific state because a TM is more
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