On 2024-02-18 15:27:38 +0000, olcott said:
On 2/18/2024 4:46 AM, Mikko wrote:
On 2024-02-17 14:59:34 +0000, olcott said:
On 2/17/2024 4:08 AM, Mikko wrote:
On 2024-02-16 19:54:06 +0000, Ben Bacarisse said:
Mikko <[email protected]> writes:
On 2024-02-16 11:43:15 +0000, Ben Bacarisse said:
Mikko <[email protected]> writes:
On 2024-02-16 06:07:04 +0000, olcott said:
// Linz Turing machine H --- M applied to w
// --- Does M halts on w?
H.q0 ⟨M⟩ w ⊢* H.qy // M applied to w halts
H.q0 ⟨M⟩ w ⊢* Hqn // M applied to w does not halt
// Linz Turing machine H --- H applied to ⟨H⟩
// --- Do you halt on your own Turing Machine description ?
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qy // H applied to ⟨H⟩ halts >>>>>>>>> H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qn // H applied to ⟨H⟩ does not halt >>>>>>>> What does H applied to <H> mean? H requires two argumlents.
Do you mean that the unspecified second argument is the empty tape? >>>>>>>> Linz always specifies both arguments of H.
Turing machines don't have "arguments" -- there is just a tape.
Personally, I would prefer a bit more rigour with an explicit notation >>>>>>> for the encoding of a pair[1], but Linz is outlining this proof only >>>>>>> because is has some historical interest.
When discussing a Turing machine it may be practical to call the
initial tape content a sequence of arguments if the problem
specification specifies the input as a combination of separately
defined parts.
Yes, but that won't help here because you are asking what "H applied to >>>>> <H>" might mean. All TM's only require a string, even though in some >>>>> cases it's convenient to pretend that there is a sequence of
"arguments".
What follows the words "applied to" must specify an input to the
Turing machine identified before those words. Linz does not say
what H is expected to do if the input is not a pair of descritions,
a Turing machine and a tape content. Therefore, whoever says
"H applied to <H>" must tell what that means, in particular,
whether H may answer something else that "yes" or "not".
Maybe you should read Linz
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
Linz uses Wm as the TM description of M
// Verbatim Linz Turing machine H --- M applied to w
// --- Does M halt on w?
H.q0 Wm w ⊢* H.qy // M applied to w halts
H.q0 Wm w ⊢* H.qn // M applied to w does not halt
A particular caseof this is
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qy // H applied to ⟨H⟩ halts
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qn // H applied to ⟨H⟩ does not halt
which you said above. However, Linz does not specify whether
H applied to <H> should halt or not, as the input is not in
the domain of H, so nothing can be inferred from this case,
which therefore is uninteresting.
"Turing machine H will halt with either a yes or no answer.
We achieve this by asking that H halt in one of two
corresponding final states, say, qy or qn." https://liarparadox.org/Peter_Linz_HP(Pages_318-319).pdf
Your quote is wrong. A partial sentence should not be quoted
without a good reason and when there q good reason to omit
a part of a sentence the omission should be clearly indicated
(usually with trhree dots).
--
Mikko
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