olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because
it contradicts the definition of a computer science decider in some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by everyone
by you (i.e. about which computations are finite and which are not) is
indeed undecidable.
You are even (almost) correct about the halting theorem. The two
notions of "computation" and "halt decider", as conventionally defined,
are contradictory.
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because
it contradicts the definition of a computer science decider in some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by everyone
by you (i.e. about which computations are finite and which are not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting problem definition so that it does not diverge from the definition of a decider
thus causes it to diverge from the definition of a computation.
You are even (almost) correct about the halting theorem. The two
notions of "computation" and "halt decider", as conventionally defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an input, whether the program *specified by this description* will finish running, or continue to run forever. https://en.wikipedia.org/wiki/Halting_problem
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because >>>> it contradicts the definition of a computer science decider in some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by everyone
by you (i.e. about which computations are finite and which are not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting problem
definition so that it does not diverge from the definition of a
decider thus causes it to diverge from the definition of a computation.
You are even (almost) correct about the halting theorem. The two
notions of "computation" and "halt decider", as conventionally defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and
an input, whether the program *specified by this description* will
finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
You are just proving that you don't understand the nature of logic, or
of Truth.
The Halting Problem STARTS with some arbitrary program. If that program
can't be specified to the "decider", then the decider just fails to be
an answer to the Halting Problem.
Otherwise, I can trivially write a "correct" halt decider by just
defining that it can accept a very limited set of encoded programs (like
none with backward jumps), and then I can easily decide if they will
halt or not.
This example shows the incorrectness of YOUR (false) definition.
You just continue to prove your ignorance of the field.
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because >>>>> it contradicts the definition of a computer science decider in some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by everyone >>>> by you (i.e. about which computations are finite and which are not) is >>>> indeed undecidable.
Not at all. We must simply correct the error of the halting problem
definition so that it does not diverge from the definition of a
decider thus causes it to diverge from the definition of a computation.
You are even (almost) correct about the halting theorem. The two
notions of "computation" and "halt decider", as conventionally defined, >>>> are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and
an input, whether the program *specified by this description* will
finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other then computer science itself is an inconsistent system thus conclusively
proving that computer science diverges from correct reasoning.
If all halt deciders must compute the mapping from their inputs to an accept/reject state on the basis of the actual behavior that this input actually specifies and the halting problem specifies that a halt decider
must compute the mapping from non-inputs, then one of these two must go
or computer science remains inconsistent.
learned-by-rote people that only know things by-the-book tend to take
the gospel of textbooks as holy words contradictions and all.
Like with religious people they tend to believe that the contradictions
are somehow resolved at a level higher than their current understanding.
You are just proving that you don't understand the nature of logic, or
of Truth.
The Halting Problem STARTS with some arbitrary program. If that
program can't be specified to the "decider", then the decider just
fails to be an answer to the Halting Problem.
Otherwise, I can trivially write a "correct" halt decider by just
defining that it can accept a very limited set of encoded programs
(like none with backward jumps), and then I can easily decide if they
will halt or not.
This example shows the incorrectness of YOUR (false) definition.
You just continue to prove your ignorance of the field.
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong
because
it contradicts the definition of a computer science decider in some >>>>>> rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by everyone >>>>> by you (i.e. about which computations are finite and which are not) is >>>>> indeed undecidable.
Not at all. We must simply correct the error of the halting problem
definition so that it does not diverge from the definition of a
decider thus causes it to diverge from the definition of a computation. >>>>
You are even (almost) correct about the halting theorem. The two
notions of "computation" and "halt decider", as conventionally
defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and
an input, whether the program *specified by this description* will
finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other then
computer science itself is an inconsistent system thus conclusively
proving that computer science diverges from correct reasoning.
If all halt deciders must compute the mapping from their inputs to an
accept/reject state on the basis of the actual behavior that this
input actually specifies and the halting problem specifies that a halt
decider must compute the mapping from non-inputs, then one of these
two must go or computer science remains inconsistent.
learned-by-rote people that only know things by-the-book tend to take
the gospel of textbooks as holy words contradictions and all.
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their
current understanding.
Except that you are ignoring that the definitions are NOT inconsistent, unless you require that Halting be computable.
The Halting Mapping of Turing Machines is well defined, as a mapping of
a Turing Machine + finite String Input -> { Halting, Non-Halting} based
on if the Turing Machine will reach a final state in any finite number
of steps, or never reach such a final state after an unbounded number of step.
Right? That is a very straight forward definition, and all Inputs have a
well defined and definite output. No Machine + Input can do both be
Halting and Non-Halting, or fail to be at least one of Halting or Non-Halting. (Either then number of steps processed halts at a finite
number in a final state or counts to an unbounded number).
A Decider, always maps an input (in its domain) to an output (in its
range). The quesiton of the Halting Problem is does there exist a
Decider that its input -> output map matches the Halting Mapping.
Since a decider in this case is a Turing Machine, we know that its input
is a string in a given alphabet, so the question comes, can we alway
express a Turing Machine as a finite string representation, and the
answer to that is YES. (Maybe not in all alphabets, but there exist
alphabets that can express them).
This is because BY DEFINITON, a Turing Machine has a finite number of
states, and accepts a tape with a finite alphabet, thus we have a finite number of states * a fintie number if symbols at the tape head giving a finite number of cases specifying a finite state, a finite symbol, and a binary tape motion. This is thus expressable in a finite string.
Thus we can ALWAYS convert the input to the Halting Mapping into some
input that FULLY EXPRESSES what the input is, thus there exists machines
with a range that expresses ALL possible Turing Machine + Input possibilities. We actually knew that before from the existence of the Universal Turing Machine, which takes as its input such a description.
Thus, if a given machine can't "understand" its input as such a machine
in some cases, the error is in that particular machine, not the specification.
Now, yes, it is still possible that no machine can actually compute such
a mapping, but that is the question itself. Your error is you seem to be presuming that the definition of a Halt Decider requires that such a
machine actually exist, which it doesn't.
It is the same as you idea that the Truth of a statement requires that a Proof or Refutation exist, which it doesn't. (We are allowed to have
Unknown and even Unknowable Truths).
There is no conflict, just the fact that such a machine can not exist.
You are just proving that you don't understand the nature of logic,
or of Truth.
The Halting Problem STARTS with some arbitrary program. If that
program can't be specified to the "decider", then the decider just
fails to be an answer to the Halting Problem.
Otherwise, I can trivially write a "correct" halt decider by just
defining that it can accept a very limited set of encoded programs
(like none with backward jumps), and then I can easily decide if they
will halt or not.
This example shows the incorrectness of YOUR (false) definition.
You just continue to prove your ignorance of the field.
On 5/14/2022 10:33 AM, Richard Damon wrote:
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong
because
it contradicts the definition of a computer science decider in some >>>>>>> rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by
everyone
by you (i.e. about which computations are finite and which are
not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting problem
definition so that it does not diverge from the definition of a
decider thus causes it to diverge from the definition of a
computation.
You are even (almost) correct about the halting theorem. The two >>>>>> notions of "computation" and "halt decider", as conventionally
defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program
and an input, whether the program *specified by this description*
will finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other then
computer science itself is an inconsistent system thus conclusively
proving that computer science diverges from correct reasoning.
If all halt deciders must compute the mapping from their inputs to an
accept/reject state on the basis of the actual behavior that this
input actually specifies and the halting problem specifies that a
halt decider must compute the mapping from non-inputs, then one of
these two must go or computer science remains inconsistent.
learned-by-rote people that only know things by-the-book tend to take
the gospel of textbooks as holy words contradictions and all.
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their
current understanding.
Except that you are ignoring that the definitions are NOT
inconsistent, unless you require that Halting be computable.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the corresponding output. https://en.wikipedia.org/wiki/Computable_function
The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition of a computable function in some rare cases. In these cases the halting
criteria are incorrect.
The Halting Mapping of Turing Machines is well defined, as a mapping
of a Turing Machine + finite String Input -> { Halting, Non-Halting}
based on if the Turing Machine will reach a final state in any finite
number of steps, or never reach such a final state after an unbounded
number of step.
It must be the actual behavior actually specified by the inputs and
cannot be the behavior specified by non-inputs unless this behavior is identical to the behavior of the inputs.
It has previously simply always been (incorrectly) assumed to be the
case that the behavior specified by the inputs cannot possibly diverge
from the behavior of their direct execution.
In those cases where the actual behavior of the actual input to H(P,P)
is not identical to the behavior of the direct execution of P(P) the definition of the halting criteria directly contradicts the definition
of a decider and the definition of a computation, thus invalidating it.
On 5/14/22 12:52 PM, olcott wrote:
On 5/14/2022 10:33 AM, Richard Damon wrote:
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>> because
it contradicts the definition of a computer science decider in some >>>>>>>> rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by
everyone
by you (i.e. about which computations are finite and which are
not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting
problem definition so that it does not diverge from the definition >>>>>> of a decider thus causes it to diverge from the definition of a
computation.
You are even (almost) correct about the halting theorem. The two >>>>>>> notions of "computation" and "halt decider", as conventionally
defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program
and an input, whether the program *specified by this description*
will finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other
then computer science itself is an inconsistent system thus
conclusively proving that computer science diverges from correct
reasoning.
If all halt deciders must compute the mapping from their inputs to
an accept/reject state on the basis of the actual behavior that this
input actually specifies and the halting problem specifies that a
halt decider must compute the mapping from non-inputs, then one of
these two must go or computer science remains inconsistent.
learned-by-rote people that only know things by-the-book tend to
take the gospel of textbooks as holy words contradictions and all.
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their
current understanding.
Except that you are ignoring that the definitions are NOT
inconsistent, unless you require that Halting be computable.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the
corresponding output. https://en.wikipedia.org/wiki/Computable_function
The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition of a
computable function in some rare cases. In these cases the halting
criteria are incorrect.
You just don't understand do you. The Halting Criteria is NOT defined as
a "Computable Function", so can't be in conflict with the definition of
a decider.
In fact, the question is "Is the Halting Function
Commputable?" This means that if the definition of the Halting Criteria
is incompatible with making a computation from it, we get the simple
answer of "No, the Halting Function is not computable"
You don't seem to understnad that not all functions are computatable,
and that for those that answer to the question of can you make a Turing Machine compute them is just "No".
The Halting Mapping of Turing Machines is well defined, as a mapping
of a Turing Machine + finite String Input -> { Halting, Non-Halting}
based on if the Turing Machine will reach a final state in any finite
number of steps, or never reach such a final state after an unbounded
number of step.
It must be the actual behavior actually specified by the inputs and
cannot be the behavior specified by non-inputs unless this behavior is
identical to the behavior of the inputs.
Right, and since the input specifies all the details of the Turing
Machine in question, the "behavior" of that input relates to that machine.
That IS the input, not a non-input. In fact, YOUR example asks about a non-input, as P calls H which isn't provided in the input, and thus it
is invalid for your H to answer about that behavior.
It has previously simply always been (incorrectly) assumed to be the
case that the behavior specified by the inputs cannot possibly diverge
from the behavior of their direct execution.
Because BY DEFINITION, it CAN'T, or the decider doesn't meet the requriements.
In those cases where the actual behavior of the actual input to H(P,P)
is not identical to the behavior of the direct execution of P(P) the
definition of the halting criteria directly contradicts the definition
of a decider and the definition of a computation, thus invalidating it.
Nope, it proves that your H fails to meet the requriements. After all,
the input DOES specify the behavior being asked about, if it was
constructed correctly as a representation of the machine in question.
Thus any error is on the decider or the person who designed it and the representation specification.
Note, DEFINITIONS CAN NOT BE INVALID.
There is no contradiction between the definition of a decider and the
Halting Problem, only the fact that no decider can exist that meets the requirements
If you can't handle that, then that is YOUR problem, not the logic systems.
On 5/14/2022 4:28 PM, Richard Damon wrote:
On 5/14/22 12:52 PM, olcott wrote:
On 5/14/2022 10:33 AM, Richard Damon wrote:
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>>> because
it contradicts the definition of a computer science decider in >>>>>>>>> some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by >>>>>>>> everyone
by you (i.e. about which computations are finite and which are >>>>>>>> not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting
problem definition so that it does not diverge from the
definition of a decider thus causes it to diverge from the
definition of a computation.
You are even (almost) correct about the halting theorem. The two >>>>>>>> notions of "computation" and "halt decider", as conventionally >>>>>>>> defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program >>>>>>> and an input, whether the program *specified by this description* >>>>>>> will finish running, or continue to run forever.
https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other
then computer science itself is an inconsistent system thus
conclusively proving that computer science diverges from correct
reasoning.
If all halt deciders must compute the mapping from their inputs to
an accept/reject state on the basis of the actual behavior that
this input actually specifies and the halting problem specifies
that a halt decider must compute the mapping from non-inputs, then
one of these two must go or computer science remains inconsistent.
learned-by-rote people that only know things by-the-book tend to
take the gospel of textbooks as holy words contradictions and all.
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their
current understanding.
Except that you are ignoring that the definitions are NOT
inconsistent, unless you require that Halting be computable.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return
the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition of
a computable function in some rare cases. In these cases the halting
criteria are incorrect.
You just don't understand do you. The Halting Criteria is NOT defined
as a "Computable Function", so can't be in conflict with the
definition of a decider.
So in this same way we can make another undecidable problem in computer science: there is no "box of oreos" in computer science that can compute
the length of a finite string in the same way that there is no non-computation that can compute halting.
On 5/14/2022 5:56 PM, Richard Damon wrote:
On 5/14/22 5:53 PM, olcott wrote:
On 5/14/2022 4:28 PM, Richard Damon wrote:
On 5/14/22 12:52 PM, olcott wrote:
On 5/14/2022 10:33 AM, Richard Damon wrote:
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is >>>>>>>>>>> wrong because
it contradicts the definition of a computer science decider >>>>>>>>>>> in some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by >>>>>>>>>> everyone
by you (i.e. about which computations are finite and which are >>>>>>>>>> not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting
problem definition so that it does not diverge from the
definition of a decider thus causes it to diverge from the
definition of a computation.
You are even (almost) correct about the halting theorem. The two >>>>>>>>>> notions of "computation" and "halt decider", as conventionally >>>>>>>>>> defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of >>>>>>>>> determining, from a description of an arbitrary computer
program and an input, whether the program *specified by this >>>>>>>>> description* will finish running, or continue to run forever. >>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other >>>>>>> then computer science itself is an inconsistent system thus
conclusively proving that computer science diverges from correct >>>>>>> reasoning.
If all halt deciders must compute the mapping from their inputs
to an accept/reject state on the basis of the actual behavior
that this input actually specifies and the halting problem
specifies that a halt decider must compute the mapping from
non-inputs, then one of these two must go or computer science
remains inconsistent.
learned-by-rote people that only know things by-the-book tend to >>>>>>> take the gospel of textbooks as holy words contradictions and all. >>>>>>>
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their >>>>>>> current understanding.
Except that you are ignoring that the definitions are NOT
inconsistent, unless you require that Halting be computable.
Computable functions are the basic objects of study in
computability theory. Computable functions are the formalized
analogue of the intuitive notion of algorithms, in the sense that a
function is computable if there exists an algorithm that can do the
job of the function, i.e. given an input of the function domain it
can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition
of a computable function in some rare cases. In these cases the
halting criteria are incorrect.
You just don't understand do you. The Halting Criteria is NOT
defined as a "Computable Function", so can't be in conflict with the
definition of a decider.
So in this same way we can make another undecidable problem in
computer science: there is no "box of oreos" in computer science that
can compute the length of a finite string in the same way that there
is no non-computation that can compute halting.
Another of your famous nonsensical diversions. Since there IS NO "box
of oreos" in Computer Science, you just committed another category
error proving you don't know what you are talking about.
In this same way requiring a non-computation to compute is an incorrect problem definition.
On 5/14/22 5:53 PM, olcott wrote:
On 5/14/2022 4:28 PM, Richard Damon wrote:
On 5/14/22 12:52 PM, olcott wrote:
On 5/14/2022 10:33 AM, Richard Damon wrote:
On 5/14/22 10:53 AM, olcott wrote:
On 5/14/2022 9:31 AM, Richard Damon wrote:
On 5/14/22 10:00 AM, olcott wrote:
On 5/14/2022 3:07 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>>>> because
it contradicts the definition of a computer science decider in >>>>>>>>>> some
rare cases that no one never noticed before.
Well that's pretty clear. The halting problem, as defined by >>>>>>>>> everyone
by you (i.e. about which computations are finite and which are >>>>>>>>> not) is
indeed undecidable.
Not at all. We must simply correct the error of the halting
problem definition so that it does not diverge from the
definition of a decider thus causes it to diverge from the
definition of a computation.
You are even (almost) correct about the halting theorem. The two >>>>>>>>> notions of "computation" and "halt decider", as conventionally >>>>>>>>> defined,
are contradictory.
*The corrected halting problem definition*
In computability theory, the halting problem is the problem of >>>>>>>> determining, from a description of an arbitrary computer program >>>>>>>> and an input, whether the program *specified by this
description* will finish running, or continue to run forever. >>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
WRONG, you don't get to change the definition of the Problem.
[ computer science is inconsistent ]
If two definitions within computer science contradict each other
then computer science itself is an inconsistent system thus
conclusively proving that computer science diverges from correct
reasoning.
If all halt deciders must compute the mapping from their inputs to >>>>>> an accept/reject state on the basis of the actual behavior that
this input actually specifies and the halting problem specifies
that a halt decider must compute the mapping from non-inputs, then >>>>>> one of these two must go or computer science remains inconsistent. >>>>>>
learned-by-rote people that only know things by-the-book tend to
take the gospel of textbooks as holy words contradictions and all. >>>>>>
Like with religious people they tend to believe that the
contradictions are somehow resolved at a level higher than their
current understanding.
Except that you are ignoring that the definitions are NOT
inconsistent, unless you require that Halting be computable.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return
the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
The halting criteria are defined such that they diverge from the
definition of a decider and they also diverge form the definition of
a computable function in some rare cases. In these cases the halting
criteria are incorrect.
You just don't understand do you. The Halting Criteria is NOT defined
as a "Computable Function", so can't be in conflict with the
definition of a decider.
So in this same way we can make another undecidable problem in
computer science: there is no "box of oreos" in computer science that
can compute the length of a finite string in the same way that there
is no non-computation that can compute halting.
Another of your famous nonsensical diversions. Since there IS NO "box of oreos" in Computer Science, you just committed another category error
proving you don't know what you are talking about.
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such that
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because >>>>>> it contradicts the definition of a computer science decider in some >>>>>> rare cases that no one never noticed before.Well that's pretty clear. The halting problem, as defined by everyone >>>>> by you (i.e. about which computations are finite and which are not) is >>>>> indeed undecidable.
Not at all.
D(X,Y) == true if and only of X(Y) halts and false otherwise?
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it
must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y).
That's what they specify in the call D(X,Y) that you are trying so hard
to avoid taking about. What you take them to specify in a call to your
H is not interesting.
Your H is boring because "the computations that input specify" are so limited. Many simple computations consisting of one pointer called with
the other as an argument can't be specified at all (apparently) so you
should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and only
of the computation, X(Y), specified by those "inputs" does not halt, or
there can't be. But even after 18 years of what you call "research" you won't dare hazard a guess about the possible existence of such an
important algorithm!
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such that >>>> D(X,Y) == true if and only of X(Y) halts and false otherwise?
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrongWell that's pretty clear. The halting problem, as defined by
because
it contradicts the definition of a computer science decider in some >>>>>>> rare cases that no one never noticed before.
everyone
by you (i.e. about which computations are finite and which are
not) is
indeed undecidable.
Not at all.
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it
must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y).
Not when they are correctly simulated by H.
That's what they specify in the call D(X,Y) that you are trying so hard
to avoid taking about. What you take them to specify in a call to your
H is not interesting.
Your H is boring because "the computations that input specify" are so
limited. Many simple computations consisting of one pointer called with
the other as an argument can't be specified at all (apparently) so you
should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and only
of the computation, X(Y), specified by those "inputs" does not halt, or
there can't be. But even after 18 years of what you call "research" you
won't dare hazard a guess about the possible existence of such an
important algorithm!
You continue to push the nutty idea that the halt decider is required to "compute" on non-computation.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the corresponding output. https://en.wikipedia.org/wiki/Computable_function
On 5/17/22 11:02 PM, olcott wrote:
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such that >>>>> D(X,Y) == true if and only of X(Y) halts and false otherwise?
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>> becauseWell that's pretty clear. The halting problem, as defined by
it contradicts the definition of a computer science decider in some >>>>>>>> rare cases that no one never noticed before.
everyone
by you (i.e. about which computations are finite and which are
not) is
indeed undecidable.
Not at all.
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it
must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y).
Not when they are correctly simulated by H.
That's what they specify in the call D(X,Y) that you are trying so hard
to avoid taking about. What you take them to specify in a call to your >>> H is not interesting.
Your H is boring because "the computations that input specify" are so
limited. Many simple computations consisting of one pointer called with >>> the other as an argument can't be specified at all (apparently) so you
should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and only
of the computation, X(Y), specified by those "inputs" does not halt, or
there can't be. But even after 18 years of what you call "research" you >>> won't dare hazard a guess about the possible existence of such an
important algorithm!
You continue to push the nutty idea that the halt decider is required to
"compute" on non-computation.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return the
corresponding output. https://en.wikipedia.org/wiki/Computable_function
If H^ is not a computation, then H isn't either.
You are just proving that you don't understand what this topic is about.
It has been shown that you can convert ANY Turing Machine to a representation, and the input to H is defined as a Representation of a
Turing Machine.
If you arguement is that you can't decide on the behavior of a Turing
Machine just from a representation of it as a computation, then you are
just agreeing that the Halting Problem IS impossible to "Compute" even
if you don't understand that is what you are saying.
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such that >>>> D(X,Y) == true if and only of X(Y) halts and false otherwise?
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong because >>>>>>> it contradicts the definition of a computer science decider in some >>>>>>> rare cases that no one never noticed before.Well that's pretty clear. The halting problem, as defined by everyone >>>>>> by you (i.e. about which computations are finite and which are not) is >>>>>> indeed undecidable.
Not at all.
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it
must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y).
Not when they are correctly simulated by H.
That's what they specify in the call D(X,Y) that you are trying so hard
to avoid taking about.
You continue to push the nutty idea that the halt decider is required to "compute" on non-computation.
On 5/18/2022 7:27 AM, Richard Damon wrote:
On 5/17/22 11:02 PM, olcott wrote:
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>>> becauseWell that's pretty clear. The halting problem, as defined by >>>>>>>> everyone
it contradicts the definition of a computer science decider in >>>>>>>>> some
rare cases that no one never noticed before.
by you (i.e. about which computations are finite and which are >>>>>>>> not) is
indeed undecidable.
Not at all.
that
D(X,Y) == true if and only of X(Y) halts and false otherwise?
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it
must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y).
Not when they are correctly simulated by H.
That's what they specify in the call D(X,Y) that you are trying so hard >>>> to avoid taking about. What you take them to specify in a call to your >>>> H is not interesting.
Your H is boring because "the computations that input specify" are so
limited. Many simple computations consisting of one pointer called
with
the other as an argument can't be specified at all (apparently) so you >>>> should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and only >>>> of the computation, X(Y), specified by those "inputs" does not halt, or >>>> there can't be. But even after 18 years of what you call "research"
you
won't dare hazard a guess about the possible existence of such an
important algorithm!
You continue to push the nutty idea that the halt decider is required to >>> "compute" on non-computation.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return
the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
If H^ is not a computation, then H isn't either.
H(P,P)==0 is a correct computation.
You are just proving that you don't understand what this topic is about.
It has been shown that you can convert ANY Turing Machine to a
representation, and the input to H is defined as a Representation of a
Turing Machine.
int sum(int x, int y)
{
return x + y;
}
H(P,P) (a dependent computation) cannot report on P(P) an independent computation in the same way that sum(3,4) cannot report on sum(8,7).
If you arguement is that you can't decide on the behavior of a Turing
Machine just from a representation of it as a computation, then you
are just agreeing that the Halting Problem IS impossible to "Compute"
even if you don't understand that is what you are saying.
On 5/18/22 11:37 AM, olcott wrote:
On 5/18/2022 7:27 AM, Richard Damon wrote:
On 5/17/22 11:02 PM, olcott wrote:
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:Not when they are correctly simulated by H.
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written such >>>>>>> that
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is wrong >>>>>>>>>> becauseWell that's pretty clear. The halting problem, as defined by >>>>>>>>> everyone
it contradicts the definition of a computer science decider in >>>>>>>>>> some
rare cases that no one never noticed before.
by you (i.e. about which computations are finite and which are >>>>>>>>> not) is
indeed undecidable.
Not at all.
D(X,Y) == true if and only of X(Y) halts and false otherwise?
In the same way that a TM can use a "box of oreos" to compute the
length of a finite string a non-computation can compute the halt
status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it >>>>>> must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call X(Y). >>>>
That's what they specify in the call D(X,Y) that you are trying so
hard
to avoid taking about. What you take them to specify in a call to
your
H is not interesting.
Your H is boring because "the computations that input specify" are so >>>>> limited. Many simple computations consisting of one pointer called >>>>> with
the other as an argument can't be specified at all (apparently) so you >>>>> should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and only >>>>> of the computation, X(Y), specified by those "inputs" does not
halt, or
there can't be. But even after 18 years of what you call
"research" you
won't dare hazard a guess about the possible existence of such an
important algorithm!
You continue to push the nutty idea that the halt decider is
required to
"compute" on non-computation.
Computable functions are the basic objects of study in computability
theory. Computable functions are the formalized analogue of the
intuitive notion of algorithms, in the sense that a function is
computable if there exists an algorithm that can do the job of the
function, i.e. given an input of the function domain it can return
the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
If H^ is not a computation, then H isn't either.
H(P,P)==0 is a correct computation.
Only if H isn't a Halting Decider.
Since P(P) halts when H(P,P) is 0, it CAN'T be correct.
DEFINITION.
You are just proving that you don't understand what this topic is about. >>>
It has been shown that you can convert ANY Turing Machine to a
representation, and the input to H is defined as a Representation of
a Turing Machine.
int sum(int x, int y)
{
return x + y;
}
H(P,P) (a dependent computation) cannot report on P(P) an independent
computation in the same way that sum(3,4) cannot report on sum(8,7).
So you ADMIT that there is a compuation that H can't give the answer to
the Halting Problem?
That just PROVES the Theorem you are trying to disprove.
If you arguement is that you can't decide on the behavior of a Turing
Machine just from a representation of it as a computation, then you
are just agreeing that the Halting Problem IS impossible to "Compute"
even if you don't understand that is what you are saying.
On 5/18/2022 6:09 PM, Richard Damon wrote:
On 5/18/22 11:37 AM, olcott wrote:
On 5/18/2022 7:27 AM, Richard Damon wrote:
On 5/17/22 11:02 PM, olcott wrote:
On 5/15/2022 7:18 AM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 6:20 PM, Ben wrote:
olcott <NoOne@NoWhere.com> writes:
On 5/14/2022 3:07 AM, Ben wrote:So you believe it is possible for a function D to be written
olcott <NoOne@NoWhere.com> writes:
The halting criteria that the halting problem expects is >>>>>>>>>>> wrong becauseWell that's pretty clear. The halting problem, as defined by >>>>>>>>>> everyone
it contradicts the definition of a computer science decider >>>>>>>>>>> in some
rare cases that no one never noticed before.
by you (i.e. about which computations are finite and which are >>>>>>>>>> not) is
indeed undecidable.
Not at all.
such that
D(X,Y) == true if and only of X(Y) halts and false otherwise?
In the same way that a TM can use a "box of oreos" to compute the >>>>>>> length of a finite string a non-computation can compute the halt >>>>>>> status of a non-input.
The HP is defined incorrectly. It cannot be about computations, it >>>>>>> must be about the computations that inputs specify.
The two pointers X and Y can be taken to specify a function call
X(Y).
Not when they are correctly simulated by H.
That's what they specify in the call D(X,Y) that you are trying so >>>>>> hard
to avoid taking about. What you take them to specify in a call to >>>>>> your
H is not interesting.
Your H is boring because "the computations that input specify" are so >>>>>> limited. Many simple computations consisting of one pointer
called with
the other as an argument can't be specified at all (apparently) so >>>>>> you
should probably stop wasting time on your H.
Either there can be a function D such that D(X,Y) == false if and
only
of the computation, X(Y), specified by those "inputs" does not
halt, or
there can't be. But even after 18 years of what you call
"research" you
won't dare hazard a guess about the possible existence of such an
important algorithm!
You continue to push the nutty idea that the halt decider is
required to
"compute" on non-computation.
Computable functions are the basic objects of study in
computability theory. Computable functions are the formalized
analogue of the intuitive notion of algorithms, in the sense that a
function is computable if there exists an algorithm that can do the
job of the function, i.e. given an input of the function domain it
can return the corresponding output.
https://en.wikipedia.org/wiki/Computable_function
If H^ is not a computation, then H isn't either.
H(P,P)==0 is a correct computation.
Only if H isn't a Halting Decider.
Your definition of halt decider contradicts the definition of a decider
and also contradicts the definition of a computation, thus is incorrect.
When we restrict the definition of a halt decider to a computation then H(P,P)==0 is a correct computation by a decider.
a function is computable if there exists an algorithm that can do the
job of the function, i.e. given an input of the function domain it can
return the corresponding output. https://en.wikipedia.org/wiki/Computable_function
Since P(P) halts when H(P,P) is 0, it CAN'T be correct.
DEFINITION.
You are just proving that you don't understand what this topic is
about.
It has been shown that you can convert ANY Turing Machine to a
representation, and the input to H is defined as a Representation of
a Turing Machine.
int sum(int x, int y)
{
return x + y;
}
H(P,P) (a dependent computation) cannot report on P(P) an independent
computation in the same way that sum(3,4) cannot report on sum(8,7).
So you ADMIT that there is a compuation that H can't give the answer
to the Halting Problem?
That just PROVES the Theorem you are trying to disprove.
;
If you arguement is that you can't decide on the behavior of a
Turing Machine just from a representation of it as a computation,
then you are just agreeing that the Halting Problem IS impossible to
"Compute" even if you don't understand that is what you are saying.
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