Re: Incorrect requirements --- Computing the mapping from the input to HHH(DD)

On 5/10/2025 4:42 PM, olcott wrote:

On 5/10/2025 3:22 PM, Alan Mackenzie wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

On Sat, 10 May 2025 18:48:12 +0000, Alan Mackenzie wrote:

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olcott <polcott333@gmail.com> wrote:

On 5/10/2025 7:37 AM, Bonita Montero wrote:

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[ .... ]

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I guess that not even a professor of theoretical computer science
would spend years working on so few lines of code.

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I created a whole x86utm operating system.
It correctly determines that the halting problem's otherwise
"impossible" input is actually non halting.

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You've spent over 20 years on this matter.  Compare this with Alan
Turing's solution of the Entscheidungsproblem.  He published this in
1936 when he was just 24 years old.

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Turing didn't solve anything: what he published contained a mistake: the
category (type) error that I have described previously in this forum.

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OK, then, give the page and line numbers from Turing's 1936 paper where
this alleged mistake was made.  I would be surprised indeed if you'd even
looked at Turing's paper, far less understood it.  Yet you're ready to
denigrate his work.
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Perhaps it is time for you to withdraw these uncalled for insinuations.
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/Flibble

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 It is the whole gist of the entire idea of
the halting problem proof that is wrongheaded.
 (1) It is anchored in the false assumption that an
input to a termination analyzer can actually
do this opposite of whatever value that this
analyzer returns.

Not an assumption, but proven through a series of truth preserving operations, starting from the assumption that an algorithm exists that meets these requirements:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
A contradiction follows from that, proving that no algorithm exists that meets the above requirements, as Linz and others have proved and you have *explicitly* agreed is correct.