On 2024-02-16 15:07:17 +0000, olcott said:

On 2/16/2024 4:09 AM, Mikko wrote:

On 2024-02-16 05:42:40 +0000, olcott said:

// 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

The conditions after the // are incorrect: H must be applied to a
pair, not just <H> or some other singlet.

I am merely using different notational conventions that
are easier to understand because they are more conventional.
Linz uses Wm as the finite string Turing machine description
of some arbitrary machine M.

Your conventions are not easier to understand. I do understand what
H applied to <H> <H> means but not what H applied to <H> means.

--
Mikko

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On 2024-02-16 15:34:52 +0000, olcott said:

On 2/16/2024 9:07 AM, olcott wrote:

On 2/16/2024 4:09 AM, Mikko wrote:

On 2024-02-16 05:42:40 +0000, olcott said:

// 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

The conditions after the // are incorrect: H must be applied to a
pair, not just <H> or some other singlet.

I am merely using different notational conventions that
are easier to understand because they are more conventional.
Linz uses Wm as the finite string Turing machine description
of some arbitrary machine M.

// 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

I use ⟨M⟩ as the finite string Turing machine description
of the specific machine M.

// Linz Turing machine H --- M applied to w
// --- Does M halt 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 --- M applied to ⟨M⟩
// --- Does M halt on ⟨M⟩?
H.q0 ⟨M⟩ ⟨M⟩ ⊢* H.qy // M applied to ⟨M⟩ halts
H.q0 ⟨M⟩ ⟨M⟩ ⊢* Hqn  // M applied to ⟨M⟩ does not halt

*This syntax has been corrected because H has two parameters*

// Linz Turing machine H ---  H applied to ⟨H⟩
// --- Do you halt on your own Turing Machine description ?
H.q0 ⟨H⟩ ⟨H⟩ ⟨H⟩ ⊢* H.qy // H applied to ⟨H⟩ ⟨H⟩ halts >> H.q0 ⟨H⟩ ⟨H⟩ ⟨H⟩ ⊢* H.qn // H applied to ⟨H⟩ ⟨H⟩ does not halt

There is no specification of what should happen after H.q0 <H> <H> <H>.

--
Mikko

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Mikko <[email protected]> writes:

On 2024-02-16 15:07:17 +0000, olcott said:

On 2/16/2024 4:09 AM, Mikko wrote:

On 2024-02-16 05:42:40 +0000, olcott said:

// 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

The conditions after the // are incorrect: H must be applied to a
pair, not just <H> or some other singlet.

I am merely using different notational conventions that
are easier to understand because they are more conventional.
Linz uses Wm as the finite string Turing machine description
of some arbitrary machine M.

Your conventions are not easier to understand. I do understand what
H applied to <H> <H> means but not what H applied to <H> means.

I'm not sure why you are having trouble with that. I think it may be
down to PO's confusing use of comment syntax, suggesting that the words
are explaining the initial configuration. But that is not how PO has
been using them for that last wasted decade or two. They are
transcriptions of the conditions under which the computation unfolds as
shown. For example, for a prime number decider:

P <n> |-* qy // if <n> is a string representing a prime number, n
P <n> |-* qn // otherwise.

Linz write the conditions in the text just after the elaborated
computation, but PO took to adding them on the line using // because he
thinks it looks more "sciencey".

--
Ben.

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