On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:When the halting problem requires a halt decider
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter exmaple >>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>> therefore not relevant in that context. The halting problem
reuqires
that HHH can determine whether the counter example halts. That is, >>>>>>>> you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct argument here >>>>>>>> printf("HHH says: %s\n", Halt_Status ? "halts" : "does not >>>>>>>> halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>> do this then HHH is not a halt decider nor a partial halt decider. >>>>>>
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not justify your >>>>>> claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say "must" in
the sense that any decider that does not compute whether machine M
halts on input w is not a halt decider. But using "must" is not the
clearest way to say it because the word "must" other meanings.
It actually computes halting that this input pair specifies (⟨M⟩, >>>> w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
On 18/12/2025 06:29, olcott wrote:
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:When the halting problem requires a halt decider
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter exmaple >>>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>> reuqires
that HHH can determine whether the counter example halts. That is, >>>>>>>>> you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct argument here >>>>>>>>> printf("HHH says: %s\n", Halt_Status ? "halts" : "does not >>>>>>>>> halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>> do this then HHH is not a halt decider nor a partial halt decider. >>>>>>>
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not justify >>>>>>> your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say "must" in >>>>> the sense that any decider that does not compute whether machine M
halts on input w is not a halt decider. But using "must" is not the
clearest way to say it because the word "must" other meanings.
It actually computes halting that this input pair specifies(⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
You still havn't answered the question which textbook says "must".
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter exmaple >>>>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>> reuqires
that HHH can determine whether the counter example halts. That >>>>>>>>>> is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct argument here
printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>> not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>>> do this then HHH is not a halt decider nor a partial halt >>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not justify >>>>>>>> your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say "must" in >>>>>> the sense that any decider that does not compute whether machine M >>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>> clearest way to say it because the word "must" other meanings.
It actually computes halting that this input pair specifies(⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
--You still havn't answered the question which textbook says "must".
On 18/12/2025 15:07, olcott wrote:
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:I am trying to state the gist of this and not get so
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter >>>>>>>>>>> exmaple
mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>> reuqires
that HHH can determine whether the counter example halts. >>>>>>>>>>> That is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct argument >>>>>>>>>>> here
printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>> not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>>>> do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not
justify your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say
"must" in
the sense that any decider that does not compute whether machine M >>>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>>> clearest way to say it because the word "must" other meanings.
It actually computes halting that this input pair specifies >>>>>>> (⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt deciders. >>>>
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
You should put the whole story to GitHub. Then you can add any detail
aomeone asks. If the same quiestion is asked again you only need to
give a pointer as the answer.
--You still havn't answered the question which textbook says "must".
On 12/19/2025 4:09 AM, Mikko wrote:
On 18/12/2025 15:07, olcott wrote:
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter >>>>>>>>>>>> exmaple
mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>>> reuqires
that HHH can determine whether the counter example halts. >>>>>>>>>>>> That is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct argument >>>>>>>>>>>> here
printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>>> not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>> can't
do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not
justify your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say
"must" in
the sense that any decider that does not compute whether machine M >>>>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>>>> clearest way to say it because the word "must" other meanings. >>>>>>>>
It actually computes halting that this input pair specifies >>>>>>>> (⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt
deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
You should put the whole story to GitHub. Then you can add any detail
aomeone asks. If the same quiestion is asked again you only need to
give a pointer as the answer.
I am making one single point.
A bunch of irrelevant
questions distract away from this one point.
I have gone over these things thousands of times
and what seem obvious to me cannot possibly be
understood by anyone besides LLM systems.
These are the correct first principles of all
computation.
Computations: Transform finite strings by finite
string transformation rules into values or non-termination.
Deciders: Transform finite strings by finite string
transformation rules into {Accept, Reject}.
On 19/12/2025 16:52, olcott wrote:
On 12/19/2025 4:09 AM, Mikko wrote:
On 18/12/2025 15:07, olcott wrote:
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.
If the last sentence is true then this is not the counter >>>>>>>>>>>>> exmaple
mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>>>> reuqires
that HHH can determine whether the counter example halts. >>>>>>>>>>>>> That is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>> argument here
printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>>>> not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>>> can't
do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not >>>>>>>>>>> justify your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say >>>>>>>>> "must" in
the sense that any decider that does not compute whether machine M >>>>>>>>> halts on input w is not a halt decider. But using "must" is not >>>>>>>>> the
clearest way to say it because the word "must" other meanings. >>>>>>>>>
It actually computes halting that this input pair specifies >>>>>>>>> (⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt
deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
You should put the whole story to GitHub. Then you can add any detail
aomeone asks. If the same quiestion is asked again you only need to
give a pointer as the answer.
I am making one single point.
WHich one?
A bunch of irrelevant
questions distract away from this one point.
A sufficient answer to an irelevant question is "doesn't matter".
If a quetion is irrelevant it is sufficient to say "doesn't matter".
I have gone over these things thousands of times
and what seem obvious to me cannot possibly be
understood by anyone besides LLM systems.
These are the correct first principles of all
computation.
Computations: Transform finite strings by finite
string transformation rules into values or non-termination.
Deciders: Transform finite strings by finite string
transformation rules into {Accept, Reject}.
The terms "computation" and "decider" are not parallel. The suffix
of "decider" means that it is an agent. The word "computation" has
a diferent suffix bedause it is an action. A decider performs a
computation but it isn't one. But you can say that a decider is a
computer although more ofthen the term "automaton" is used.
One should also note that definitions are not principles.
On 12/20/2025 4:22 AM, Mikko wrote:
On 19/12/2025 16:52, olcott wrote:
On 12/19/2025 4:09 AM, Mikko wrote:
On 18/12/2025 15:07, olcott wrote:
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
If the last sentence is true then this is not the counter >>>>>>>>>>>>>> exmaple
DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH. >>>>>>>>>>>>>>
mentioned in certain proofs of noncomputability of halting >>>>>>>>>>>>>> and
therefore not relevant in that context. The halting >>>>>>>>>>>>>> problem reuqires
that HHH can determine whether the counter example halts. >>>>>>>>>>>>>> That is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>>> argument here
printf("HHH says: %s\n", Halt_Status ? "halts" : >>>>>>>>>>>>>> "does not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>>>> can't
do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
That you don't know what "category error" means does not >>>>>>>>>>>> justify your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors.
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say >>>>>>>>>> "must" in
the sense that any decider that does not compute whether
machine M
halts on input w is not a halt decider. But using "must" is >>>>>>>>>> not the
clearest way to say it because the word "must" other meanings. >>>>>>>>>>
It actually computes halting that this input pair specifies >>>>>>>>>> (⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt
deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
You should put the whole story to GitHub. Then you can add any detail
aomeone asks. If the same quiestion is asked again you only need to
give a pointer as the answer.
I am making one single point.
WHich one?
A bunch of irrelevant
questions distract away from this one point.
A sufficient answer to an irelevant question is "doesn't matter".
If a quetion is irrelevant it is sufficient to say "doesn't matter".
I have gone over these things thousands of times
and what seem obvious to me cannot possibly be
understood by anyone besides LLM systems.
These are the correct first principles of all
computation.
Computations: Transform finite strings by finite
string transformation rules into values or non-termination.
Deciders: Transform finite strings by finite string
transformation rules into {Accept, Reject}.
The terms "computation" and "decider" are not parallel. The suffix
One is a subset of the other.
of "decider" means that it is an agent. The word "computation" has
a diferent suffix bedause it is an action. A decider performs a
computation but it isn't one. But you can say that a decider is a
computer although more ofthen the term "automaton" is used.
One should also note that definitions are not principles.
A definition of computation does specify the principles
of computation.
On 20/12/2025 13:54, olcott wrote:
On 12/20/2025 4:22 AM, Mikko wrote:
On 19/12/2025 16:52, olcott wrote:
On 12/19/2025 4:09 AM, Mikko wrote:
On 18/12/2025 15:07, olcott wrote:
On 12/18/2025 5:10 AM, Mikko wrote:
On 18/12/2025 06:29, olcott wrote:When people demand too many irrelevant details
On 12/17/2025 4:41 AM, Mikko wrote:
On 15/12/2025 16:31, olcott wrote:
On 12/15/2025 3:20 AM, Mikko wrote:
On 15/12/2025 02:15, olcott wrote:
On 12/14/2025 4:46 AM, Mikko wrote:
On 11/12/2025 16:38, olcott wrote:
On 12/11/2025 2:53 AM, Mikko wrote:
olcott kirjoitti 10.12.2025 klo 18.27:
If the last sentence is true then this is not the counter >>>>>>>>>>>>>>> exmaple
DD() executed from main() calls HHH(DD) thus is >>>>>>>>>>>>>>>> not one-and-the-same-thing as an argument to HHH. >>>>>>>>>>>>>>>
mentioned in certain proofs of noncomputability of >>>>>>>>>>>>>>> halting and
therefore not relevant in that context. The halting >>>>>>>>>>>>>>> problem reuqires
that HHH can determine whether the counter example halts. >>>>>>>>>>>>>>> That is,
you must be able to replace "???" in
#include <stdio.h> // or your replacement
int main (void)
{
int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>>>> argument here
printf("HHH says: %s\n", Halt_Status ? "halts" : >>>>>>>>>>>>>>> "does not halt");
return Halt_Status;
}
with whatever specifies the behaviour of DD to HHH. If >>>>>>>>>>>>>>> you can't
do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>>>> decider.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this >>>>>>>>>>>>>> is always a category error.
That you don't know what "category error" means does not >>>>>>>>>>>>> justify your
claim. Apparently you can't apply definitions.
Turing machines only compute functions from finite
strings they never compute functions from Turing
machines.
True, but irrelevant to questions about category errors. >>>>>>>>>>>
A halt decider can at best compute the behavior of
a Turing machine through the proxy of a finite
string machine description it never computes it
directly from another Turing machine.
Whenever any textbook says that a halt decider
must compute halting for machine M on input w
is it wrong.
Which textbook actually says "must"? It is not wrong to say >>>>>>>>>>> "must" in
the sense that any decider that does not compute whether >>>>>>>>>>> machine M
halts on input w is not a halt decider. But using "must" is >>>>>>>>>>> not the
clearest way to say it because the word "must" other meanings. >>>>>>>>>>>
It actually computes halting that this input pairspecifies (⟨M⟩, w).
There is an unbalanced parenthesis above.
No halt decider ever computes the halt status
of a machine except through the proxy of finite
strings.
No halt decider computes anything because there are not halt >>>>>>>>> deciders.
I am trying to state the gist of this and not get so
bogged down in tedious details that the gist cannot
possibly ever be understood because we have too much
detail for the capacity of the human mind.
If you can't state the gist without causing more confusion than
clarity you should try something else.
I must so no.
You should put the whole story to GitHub. Then you can add any detail >>>>> aomeone asks. If the same quiestion is asked again you only need to
give a pointer as the answer.
I am making one single point.
WHich one?
A bunch of irrelevant
questions distract away from this one point.
A sufficient answer to an irelevant question is "doesn't matter".
If a quetion is irrelevant it is sufficient to say "doesn't matter".
I have gone over these things thousands of times
and what seem obvious to me cannot possibly be
understood by anyone besides LLM systems.
These are the correct first principles of all
computation.
Computations: Transform finite strings by finite
string transformation rules into values or non-termination.
Deciders: Transform finite strings by finite string
transformation rules into {Accept, Reject}.
The terms "computation" and "decider" are not parallel. The suffix
One is a subset of the other.
No, they are not. Being a subset means they share common elements. But,
as pointed out below, a decider is an agent and a computation is a non- agent. Therefore one being a subset of another requires either tant one
of the sets is empty or that there are agents that are non-agents.
of "decider" means that it is an agent. The word "computation" has
a diferent suffix bedause it is an action. A decider performs a
computation but it isn't one. But you can say that a decider is a
computer although more ofthen the term "automaton" is used.
Note that no counter argument is presented.
One should also note that definitions are not principles.
A definition of computation does specify the principles
of computation.
A definition may refer to a principle but a definition is not a
principle.
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