From Newsgroup: comp.theory

All of the textbooks require halt deciders to
report on the behavior of machine M on input w.

Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this make no difference.

We correct this error by saying that halt
deciders must report on the basis of the
behavior specified by their input finite string.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/13/25 4:07 PM, olcott wrote:

All of the textbooks require halt deciders to
report on the behavior of machine M on input w.

Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this make no difference.

We correct this error by saying that halt
deciders must report on the basis of the
behavior specified by their input finite string.

And the "behavior specified by their input finite string" *IS* the
behavior of the machine they describe. So, no problem in asking the
question as done origninally, when you understand that Turing Machines virtually always deal with a representation of the thing they are to
decide on, as few real problems are stated in terms of the arbitrary
symbol set of the Turing Machine.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 13/12/2025 23:07, olcott wrote:

All of the textbooks require halt deciders to
report on the behavior of machine M on input w.

Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this make no difference.

We correct this error by saying that halt
deciders must report on the basis of the
behavior specified by their input finite string.

That you don't quote the halting problem and that you don't quote
the definition of category error means that you don't try to
support the claim presented in the subject. It seems that you
don't even believe you could support it.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/14/2025 4:38 AM, Mikko wrote:

On 13/12/2025 23:07, olcott wrote:

All of the textbooks require halt deciders to
report on the behavior of machine M on input w.

Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this make no difference.

We correct this error by saying that halt
deciders must report on the basis of the
behavior specified by their input finite string.

That you don't quote the halting problem and that you don't quote
the definition of category error means that you don't try to
support the claim presented in the subject. It seems that you
don't even believe you could support it.

The category error is that the halting problem
requires that a halt decider report on the behavior
of a Turing machine.

An improvement would be if the halting problem
required a halt decider to report on the behavior
of a Turing machine through the proxy of a finite
string machine description.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2