All of the textbooks require halt deciders to
report on the behavior of machine M on input w.
This may be easy to understand yet not precisely
accurate.
Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this makes no functional difference.
They simply glossed over this key detail because
they thought that it made no difference.
*Defining a halt decider with perfect accuracy*
Turing machine halt deciders compute the mapping
from input finite strings to an {accept, reject}
value on the basis of the behavior that this
input finite string specifies.
On 12/13/2025 3:32 PM, olcott wrote:
All of the textbooks require halt deciders to
report on the behavior of machine M on input w.
This may be easy to understand yet not precisely
accurate.
Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this makes no functional difference.
They simply glossed over this key detail because
they thought that it made no difference.
*Defining a halt decider with perfect accuracy*
Turing machine halt deciders compute the mapping
from input finite strings to an {accept, reject}
value on the basis of the behavior that this
input finite string specifies.
By simply adding more detail we can make the
original definition more precise:
A Turing machine based halt decider reports on the
behavior of machine M on input w thorough the
proxy of the finite string machine description of
⟨M⟩ on input w.
The above seems to be more precisely accurate
than any published proof. It includes a key
detail that all of them seem to leave out.
If you know of any published proof that directly
refers to the idea of a proxy, please let me know.
On 12/13/25 5:41 PM, olcott wrote:
On 12/13/2025 3:32 PM, olcott wrote:
All of the textbooks require halt deciders to
report on the behavior of machine M on input w.
This may be easy to understand yet not precisely
accurate.
Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this makes no functional difference.
They simply glossed over this key detail because
they thought that it made no difference.
*Defining a halt decider with perfect accuracy*
Turing machine halt deciders compute the mapping
from input finite strings to an {accept, reject}
value on the basis of the behavior that this
input finite string specifies.
By simply adding more detail we can make the
original definition more precise:
A Turing machine based halt decider reports on the
behavior of machine M on input w thorough the
proxy of the finite string machine description of
⟨M⟩ on input w.
The above seems to be more precisely accurate
than any published proof. It includes a key
detail that all of them seem to leave out.
If you know of any published proof that directly
refers to the idea of a proxy, please let me know.
And the use of a string proxy is just normally assumed by the theory, as that is how Turing Machine work.
They almost ALWAYS work by a string representation proxy, as very few--
real questions are based on the "arbitrary" symbol set of the Turing Machines native operation.
If you had bothered to learn the basics of the field, you would have understood that.
Most works assume the basic knowledge of the field.
Note, even the Linz proof you mention explicitly talks about giving the decider a representation of the machine in question, the Wm as the proxy
for giving it M.
So, why did you not understand the use of a proxy.
Sometimes the problem when expressed for lay people will talk about the decider being given a description or representation of the machine.
You just reject those as you think it too vague, when it is a well
defined term, and even the general meaning is applicable, you just need
to remember that it must be a SUFFICIENT description to convey the
needed details of the machine.
On 12/13/2025 5:02 PM, Richard Damon wrote:
On 12/13/25 5:41 PM, olcott wrote:
On 12/13/2025 3:32 PM, olcott wrote:
All of the textbooks require halt deciders to
report on the behavior of machine M on input w.
This may be easy to understand yet not precisely
accurate.
Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this makes no functional difference.
They simply glossed over this key detail because
they thought that it made no difference.
*Defining a halt decider with perfect accuracy*
Turing machine halt deciders compute the mapping
from input finite strings to an {accept, reject}
value on the basis of the behavior that this
input finite string specifies.
By simply adding more detail we can make the
original definition more precise:
A Turing machine based halt decider reports on the
behavior of machine M on input w thorough the
proxy of the finite string machine description of
⟨M⟩ on input w.
The above seems to be more precisely accurate
than any published proof. It includes a key
detail that all of them seem to leave out.
If you know of any published proof that directly
refers to the idea of a proxy, please let me know.
And the use of a string proxy is just normally assumed by the theory,
as that is how Turing Machine work.
See that three agreements in one day.
That may be more than we have ever had.
Because none of the textbooks ever directly said
that the finite string input is only a proxy for
the behavior everyone always took the proxy to be
exactly one-and-the-same thing as the actual behavior.
They almost ALWAYS work by a string representation proxy, as very few
real questions are based on the "arbitrary" symbol set of the Turing
Machines native operation.
If you had bothered to learn the basics of the field, you would have
understood that.
Most works assume the basic knowledge of the field.
Note, even the Linz proof you mention explicitly talks about giving
the decider a representation of the machine in question, the Wm as the
proxy for giving it M.
So, why did you not understand the use of a proxy.
Sometimes the problem when expressed for lay people will talk about
the decider being given a description or representation of the machine.
You just reject those as you think it too vague, when it is a well
defined term, and even the general meaning is applicable, you just
need to remember that it must be a SUFFICIENT description to convey
the needed details of the machine.
On 12/13/25 9:30 PM, olcott wrote:
On 12/13/2025 5:02 PM, Richard Damon wrote:
On 12/13/25 5:41 PM, olcott wrote:
On 12/13/2025 3:32 PM, olcott wrote:
All of the textbooks require halt deciders to
report on the behavior of machine M on input w.
This may be easy to understand yet not precisely
accurate.
Since no Turing machine ever takes any Machine
M as an input this <is> a category error even
when this makes no functional difference.
They simply glossed over this key detail because
they thought that it made no difference.
*Defining a halt decider with perfect accuracy*
Turing machine halt deciders compute the mapping
from input finite strings to an {accept, reject}
value on the basis of the behavior that this
input finite string specifies.
By simply adding more detail we can make the
original definition more precise:
A Turing machine based halt decider reports on the
behavior of machine M on input w thorough the
proxy of the finite string machine description of
⟨M⟩ on input w.
The above seems to be more precisely accurate
than any published proof. It includes a key
detail that all of them seem to leave out.
If you know of any published proof that directly
refers to the idea of a proxy, please let me know.
And the use of a string proxy is just normally assumed by the theory,
as that is how Turing Machine work.
See that three agreements in one day.
That may be more than we have ever had.
Because none of the textbooks ever directly said
that the finite string input is only a proxy for
the behavior everyone always took the proxy to be
exactly one-and-the-same thing as the actual behavior.
But the behavior represented by the string *IS* exactly the behavior of
the string, so you attempted point just falls flat.
And, as I said, even your Linz book made that clear, as H took as it
input Wm (the string) not M (the machine).
Also, if you did any real study, you would have learned that the input
to the machine is almost always just a "represemtation" of the input to
the function, as we rarely are really interested in computing a result
on the strings.
The one exception is the very earliest exercises where you learn basic string manipulation with Turing Machines, but you rapidly get to wanting
to do things like "arithmatic" and then learning you need to REPRESENT numbers as something. (and a common method which baffled you as I
remember was unary, you wanted your Turing Machine to use UNICODE as it symbol set.
They almost ALWAYS work by a string representation proxy, as very few
real questions are based on the "arbitrary" symbol set of the Turing
Machines native operation.
If you had bothered to learn the basics of the field, you would have
understood that.
Most works assume the basic knowledge of the field.
Note, even the Linz proof you mention explicitly talks about giving
the decider a representation of the machine in question, the Wm as
the proxy for giving it M.
So, why did you not understand the use of a proxy.
Sometimes the problem when expressed for lay people will talk about
the decider being given a description or representation of the machine.
You just reject those as you think it too vague, when it is a well
defined term, and even the general meaning is applicable, you just
need to remember that it must be a SUFFICIENT description to convey
the needed details of the machine.
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,089 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 155:07:40 |
| Calls: | 13,921 |
| Calls today: | 2 |
| Files: | 187,021 |
| D/L today: |
3,908 files (988M bytes) |
| Messages: | 2,457,191 |