Hi!
I have an idea for a signaling simulating halt decider that forks the simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation
into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches
in parallel.
If the non-halting branch is determined to halt AND the halting branch
is determined to not halt then pathology is detected and reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the
simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation
into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches
in parallel.
If the non-halting branch is determined to halt AND the halting branch
is determined to not halt then pathology is detected and reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition of
Halt Decoding.
You also need to clarify the rules of you computation system, as you
have previously commented that it can't obey the "normal" rules used in computability theory.
Also, how does your decider determine if the branch it is following is non-halting.
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the
simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation
into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches
in parallel.
If the non-halting branch is determined to halt AND the halting branch
is determined to not halt then pathology is detected and reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition of
Halt Decoding.
It will decide that P() is pathological input and it will decide that
Px() is halting.
You also need to clarify the rules of you computation system, as you
have previously commented that it can't obey the "normal" rules used
in computability theory.
I believe you are referring to the fact that the halt decider function
and the intrinsic H(...) are a property of the machine itself, H is much
like the "move tape left" function of a Turing Machine. The only thing "abnormal" about it is that such a function is not included in the traditional definition of a Turing Machine.
Also, how does your decider determine if the branch it is following is
non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size.
/Flibble
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the
simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation
into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches
in parallel.
If the non-halting branch is determined to halt AND the halting branch
is determined to not halt then pathology is detected and reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition of
Halt Decoding.
It will decide that P() is pathological input and it will decide that
Px() is halting.
You also need to clarify the rules of you computation system, as you
have previously commented that it can't obey the "normal" rules used
in computability theory.
I believe you are referring to the fact that the halt decider function
and the intrinsic H(...) are a property of the machine itself, H is much
like the "move tape left" function of a Turing Machine. The only thing "abnormal" about it is that such a function is not included in the traditional definition of a Turing Machine.
Also, how does your decider determine if the branch it is following is
non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size.
/Flibble
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the
simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation
into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches
in parallel.
If the non-halting branch is determined to halt AND the halting branch >>>> is determined to not halt then pathology is detected and reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition of
Halt Decoding.
It will decide that P() is pathological input and it will decide that
Px() is halting.
But those are just toy programs (P was just a simple program to show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as you
have previously commented that it can't obey the "normal" rules used
in computability theory.
I believe you are referring to the fact that the halt decider function
and the intrinsic H(...) are a property of the machine itself, H is
much like the "move tape left" function of a Turing Machine. The only
thing "abnormal" about it is that such a function is not included in
the traditional definition of a Turing Machine.
Your whole model of computation is at significant variance from the
classical theoretical model.
Also, how does your decider determine if the branch it is following
is non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size.
So only able to detect non-halting in machines goig into repeating
loops, and not just that the computation keeps growing unbounded.
A very small set of the problems of normal interest in the theory.
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the >>>>> simulation into two branches if the input calls the halt decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation >>>>> into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches >>>>> in parallel.
If the non-halting branch is determined to halt AND the halting branch >>>>> is determined to not halt then pathology is detected and reported via >>>>> a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will >>>>> be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP.
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition of
Halt Decoding.
It will decide that P() is pathological input and it will decide that
Px() is halting.
But those are just toy programs (P was just a simple program to show
classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as you
have previously commented that it can't obey the "normal" rules used
in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine
itself, H is much like the "move tape left" function of a Turing
Machine. The only thing "abnormal" about it is that such a function
is not included in the traditional definition of a Turing Machine.
Your whole model of computation is at significant variance from the
classical theoretical model.
Also, how does your decider determine if the branch it is following
is non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size.
So only able to detect non-halting in machines goig into repeating
loops, and not just that the computation keeps growing unbounded.
Repeated state means a duplicate hash of the machine's finite state.
A very small set of the problems of normal interest in the theory.
The size of the set is relative. You are missing the point: to be computable the machine's resources can not be unbounded. Only problems
that are computable using the technology of the present era are of
interest: one has to be a pragmatist.
/Flibble
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks the >>>>>> simulation into two branches if the input calls the halt decider as >>>>>> per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the simulation >>>>>> into a non-halting branch (returning 0 to P) and a halting branch
(returning 1 to P) and continues the simulation of these two branches >>>>>> in parallel.
If the non-halting branch is determined to halt AND the halting
branch
is determined to not halt then pathology is detected and reported via >>>>>> a sNaP (signaling Not a Program) signal (analogous to IEEE 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that will >>>>>> be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP. >>>>>>
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition
of Halt Decoding.
It will decide that P() is pathological input and it will decide
that Px() is halting.
But those are just toy programs (P was just a simple program to show
classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as
you have previously commented that it can't obey the "normal" rules
used in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine
itself, H is much like the "move tape left" function of a Turing
Machine. The only thing "abnormal" about it is that such a function
is not included in the traditional definition of a Turing Machine.
Your whole model of computation is at significant variance from the
classical theoretical model.
Also, how does your decider determine if the branch it is following
is non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size.
So only able to detect non-halting in machines goig into repeating
loops, and not just that the computation keeps growing unbounded.
Repeated state means a duplicate hash of the machine's finite state.
But not suitable for things like the Twin Primes problem or Collatz Conjecture.
Most of the interesting problems don't end up in a simple infinite loop,
but a loop counting through numbers that will never reach there terminal condition.
>
A very small set of the problems of normal interest in the theory.
The size of the set is relative. You are missing the point: to be
computable the machine's resources can not be unbounded. Only
problems that are computable using the technology of the present era
are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern computer is unlikely to be the major limit. The "Very small set" was the number of problems that can be handled, not the physical size of the problems.
Remember, the problems that Halting was designed for were things that a person with paper and pencil were trying to solve. Detecting "simple"
loops wasn't the problem.
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that forks >>>>>>> the
simulation into two branches if the input calls the halt decider as >>>>>>> per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl;
}
When the simulator detects the call to H in P it forks the
simulation
into a non-halting branch (returning 0 to P) and a halting branch >>>>>>> (returning 1 to P) and continues the simulation of these two
branches
in parallel.
If the non-halting branch is determined to halt AND the halting
branch
is determined to not halt then pathology is detected and reported >>>>>>> via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's >>>>>>> sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that >>>>>>> will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input: >>>>>>>
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt >>>>>>> decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP. >>>>>>>
Thoughts? I am probably missing something obvious as my idea
appears to refute [Strachey 1965] and associated HP proofs which >>>>>>> great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition
of Halt Decoding.
It will decide that P() is pathological input and it will decide
that Px() is halting.
But those are just toy programs (P was just a simple program to show
classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as
you have previously commented that it can't obey the "normal"
rules used in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine
itself, H is much like the "move tape left" function of a Turing
Machine. The only thing "abnormal" about it is that such a
function is not included in the traditional definition of a Turing
Machine.
Your whole model of computation is at significant variance from the
classical theoretical model.
So only able to detect non-halting in machines goig into repeating
Also, how does your decider determine if the branch it is
following is non-halting.
The way any simulating halt decider would: through the detection of
repeated state given the machine and its resources are finite in size. >>>>
loops, and not just that the computation keeps growing unbounded.
Repeated state means a duplicate hash of the machine's finite state.
But not suitable for things like the Twin Primes problem or Collatz
Conjecture.
Most of the interesting problems don't end up in a simple infinite
loop, but a loop counting through numbers that will never reach there
terminal condition.
>
A very small set of the problems of normal interest in the theory.
The size of the set is relative. You are missing the point: to be
computable the machine's resources can not be unbounded. Only
problems that are computable using the technology of the present era
are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern computer
is unlikely to be the major limit. The "Very small set" was the number
of problems that can be handled, not the physical size of the problems.
Remember, the problems that Halting was designed for were things that
a person with paper and pencil were trying to solve. Detecting
"simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with "simple"
loops.
/Flibble
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that
forks the
simulation into two branches if the input calls the halt decider as >>>>>>>> per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>> }
When the simulator detects the call to H in P it forks the
simulation
into a non-halting branch (returning 0 to P) and a halting branch >>>>>>>> (returning 1 to P) and continues the simulation of these two
branches
in parallel.
If the non-halting branch is determined to halt AND the halting >>>>>>>> branch
is determined to not halt then pathology is detected and
reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's >>>>>>>> sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then that >>>>>>>> will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the
following case whereby the result of H is discarded by the input: >>>>>>>>
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt >>>>>>>> decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling sNaP. >>>>>>>>
Thoughts? I am probably missing something obvious as my idea >>>>>>>> appears to refute [Strachey 1965] and associated HP proofs which >>>>>>>> great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered definition >>>>>>> of Halt Decoding.
It will decide that P() is pathological input and it will decide
that Px() is halting.
But those are just toy programs (P was just a simple program to
show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as >>>>>>> you have previously commented that it can't obey the "normal"
rules used in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine
itself, H is much like the "move tape left" function of a Turing
Machine. The only thing "abnormal" about it is that such a
function is not included in the traditional definition of a Turing >>>>>> Machine.
Your whole model of computation is at significant variance from the
classical theoretical model.
Also, how does your decider determine if the branch it is
following is non-halting.
The way any simulating halt decider would: through the detection
of repeated state given the machine and its resources are finite
in size.
So only able to detect non-halting in machines goig into repeating
loops, and not just that the computation keeps growing unbounded.
Repeated state means a duplicate hash of the machine's finite state.
But not suitable for things like the Twin Primes problem or Collatz
Conjecture.
Most of the interesting problems don't end up in a simple infinite
loop, but a loop counting through numbers that will never reach there
terminal condition.
>
A very small set of the problems of normal interest in the theory.
The size of the set is relative. You are missing the point: to be
computable the machine's resources can not be unbounded. Only
problems that are computable using the technology of the present era
are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern computer
is unlikely to be the major limit. The "Very small set" was the
number of problems that can be handled, not the physical size of the
problems.
Remember, the problems that Halting was designed for were things that
a person with paper and pencil were trying to solve. Detecting
"simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with "simple"
loops.
/Flibble
Because your "repeated state" method won't catch even fairly simple
issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
On 4/23/23 8:47 AM, Mr Flibble wrote:
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:But not suitable for things like the Twin Primes problem or Collatz
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that >>>>>>>>>> forks the
simulation into two branches if the input calls the halt
decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>>> }
When the simulator detects the call to H in P it forks the >>>>>>>>>> simulation
into a non-halting branch (returning 0 to P) and a halting branch >>>>>>>>>> (returning 1 to P) and continues the simulation of these two >>>>>>>>>> branches
in parallel.
If the non-halting branch is determined to halt AND the
halting branch
is determined to not halt then pathology is detected and
reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's >>>>>>>>>> sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then >>>>>>>>>> that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>>> following case whereby the result of H is discarded by the input: >>>>>>>>>>
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt >>>>>>>>>> decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt. >>>>>>>>>> 3) Decider rejects pathological input as invalid by signaling >>>>>>>>>> sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs which >>>>>>>>>> great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered
definition of Halt Decoding.
It will decide that P() is pathological input and it will decide >>>>>>>> that Px() is halting.
But those are just toy programs (P was just a simple program to
show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the >>>>>>> following answers, its hard to see one.
You also need to clarify the rules of you computation system, >>>>>>>>> as you have previously commented that it can't obey the
"normal" rules used in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine >>>>>>>> itself, H is much like the "move tape left" function of a Turing >>>>>>>> Machine. The only thing "abnormal" about it is that such a
function is not included in the traditional definition of a
Turing Machine.
Your whole model of computation is at significant variance from
the classical theoretical model.
Also, how does your decider determine if the branch it is
following is non-halting.
The way any simulating halt decider would: through the detection >>>>>>>> of repeated state given the machine and its resources are finite >>>>>>>> in size.
So only able to detect non-halting in machines goig into
repeating loops, and not just that the computation keeps growing >>>>>>> unbounded.
Repeated state means a duplicate hash of the machine's finite state. >>>>>
Conjecture.
Most of the interesting problems don't end up in a simple infinite
loop, but a loop counting through numbers that will never reach
there terminal condition.
>
The size of the set is relative. You are missing the point: to be >>>>>> computable the machine's resources can not be unbounded. Only
A very small set of the problems of normal interest in the theory. >>>>>>
problems that are computable using the technology of the present
era are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern
computer is unlikely to be the major limit. The "Very small set"
was the number of problems that can be handled, not the physical
size of the problems.
Remember, the problems that Halting was designed for were things
that a person with paper and pencil were trying to solve. Detecting
"simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly simple
issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i" is
of finite size so it will eventually wrap around to have the same bit
pattern a second time.
/Flibble
Depends on its type. It could be a big int (infinite precision integer),
so it runs until the machine exhausts its memory.
If you are admitting that you can only handle "finite" machines, then
that has been a solved problem for a long time. Even the pathological
program can be solved under finite memory limits (it will reach memory exhaustion), which of course needs to be a fourth response possible out
of your decider.
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that
forks the
simulation into two branches if the input calls the halt
decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>> }
When the simulator detects the call to H in P it forks the
simulation
into a non-halting branch (returning 0 to P) and a halting branch >>>>>>>>> (returning 1 to P) and continues the simulation of these two >>>>>>>>> branches
in parallel.
If the non-halting branch is determined to halt AND the halting >>>>>>>>> branch
is determined to not halt then pathology is detected and
reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's >>>>>>>>> sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then
that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>> following case whereby the result of H is discarded by the input: >>>>>>>>>
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt >>>>>>>>> decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt.
3) Decider rejects pathological input as invalid by signaling >>>>>>>>> sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs which >>>>>>>>> great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered
definition of Halt Decoding.
It will decide that P() is pathological input and it will decide >>>>>>> that Px() is halting.
But those are just toy programs (P was just a simple program to
show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on the
following answers, its hard to see one.
You also need to clarify the rules of you computation system, as >>>>>>>> you have previously commented that it can't obey the "normal"
rules used in computability theory.
I believe you are referring to the fact that the halt decider
function and the intrinsic H(...) are a property of the machine
itself, H is much like the "move tape left" function of a Turing >>>>>>> Machine. The only thing "abnormal" about it is that such a
function is not included in the traditional definition of a
Turing Machine.
Your whole model of computation is at significant variance from
the classical theoretical model.
Also, how does your decider determine if the branch it is
following is non-halting.
The way any simulating halt decider would: through the detection >>>>>>> of repeated state given the machine and its resources are finite >>>>>>> in size.
So only able to detect non-halting in machines goig into repeating >>>>>> loops, and not just that the computation keeps growing unbounded.
Repeated state means a duplicate hash of the machine's finite state.
But not suitable for things like the Twin Primes problem or Collatz
Conjecture.
Most of the interesting problems don't end up in a simple infinite
loop, but a loop counting through numbers that will never reach
there terminal condition.
>
A very small set of the problems of normal interest in the theory.
The size of the set is relative. You are missing the point: to be
computable the machine's resources can not be unbounded. Only
problems that are computable using the technology of the present
era are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern
computer is unlikely to be the major limit. The "Very small set" was
the number of problems that can be handled, not the physical size of
the problems.
Remember, the problems that Halting was designed for were things
that a person with paper and pencil were trying to solve. Detecting
"simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly simple
issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i" is of finite size so it will eventually wrap around to have the same bit
pattern a second time.
/Flibble
On 23/04/2023 5:44 pm, Richard Damon wrote:
On 4/23/23 8:47 AM, Mr Flibble wrote:
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:But not suitable for things like the Twin Primes problem or
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that >>>>>>>>>>> forks the
simulation into two branches if the input calls the halt >>>>>>>>>>> decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>>>> }
When the simulator detects the call to H in P it forks the >>>>>>>>>>> simulation
into a non-halting branch (returning 0 to P) and a halting >>>>>>>>>>> branch
(returning 1 to P) and continues the simulation of these two >>>>>>>>>>> branches
in parallel.
If the non-halting branch is determined to halt AND the
halting branch
is determined to not halt then pathology is detected and >>>>>>>>>>> reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE 754's >>>>>>>>>>> sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then >>>>>>>>>>> that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>>>> following case whereby the result of H is discarded by the >>>>>>>>>>> input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a >>>>>>>>>>> halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt. >>>>>>>>>>> 3) Decider rejects pathological input as invalid by signaling >>>>>>>>>>> sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs which >>>>>>>>>>> great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered
definition of Halt Decoding.
It will decide that P() is pathological input and it will
decide that Px() is halting.
But those are just toy programs (P was just a simple program to >>>>>>>> show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on
the following answers, its hard to see one.
You also need to clarify the rules of you computation system, >>>>>>>>>> as you have previously commented that it can't obey the
"normal" rules used in computability theory.
I believe you are referring to the fact that the halt decider >>>>>>>>> function and the intrinsic H(...) are a property of the machine >>>>>>>>> itself, H is much like the "move tape left" function of a
Turing Machine. The only thing "abnormal" about it is that >>>>>>>>> such a function is not included in the traditional definition >>>>>>>>> of a Turing Machine.
Your whole model of computation is at significant variance from >>>>>>>> the classical theoretical model.
Also, how does your decider determine if the branch it is
following is non-halting.
The way any simulating halt decider would: through the
detection of repeated state given the machine and its resources >>>>>>>>> are finite in size.
So only able to detect non-halting in machines goig into
repeating loops, and not just that the computation keeps growing >>>>>>>> unbounded.
Repeated state means a duplicate hash of the machine's finite state. >>>>>>
Collatz Conjecture.
Most of the interesting problems don't end up in a simple infinite >>>>>> loop, but a loop counting through numbers that will never reach
there terminal condition.
>
The size of the set is relative. You are missing the point: to >>>>>>> be computable the machine's resources can not be unbounded. Only >>>>>>> problems that are computable using the technology of the present >>>>>>> era are of interest: one has to be a pragmatist.
A very small set of the problems of normal interest in the theory. >>>>>>>
/Flibble
For many of the problems, the "limited" memory of the modern
computer is unlikely to be the major limit. The "Very small set"
was the number of problems that can be handled, not the physical
size of the problems.
Remember, the problems that Halting was designed for were things
that a person with paper and pencil were trying to solve.
Detecting "simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly simple
issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i" is
of finite size so it will eventually wrap around to have the same bit
pattern a second time.
/Flibble
Depends on its type. It could be a big int (infinite precision
integer), so it runs until the machine exhausts its memory.
If you are admitting that you can only handle "finite" machines, then
that has been a solved problem for a long time. Even the pathological
program can be solved under finite memory limits (it will reach memory
exhaustion), which of course needs to be a fourth response possible
out of your decider.
Agree. As I posted earlier one has to be pragmatic given the finite constraints: a halt decision may not be possible on Machine A but may be possible on Machine B which has twice the resources of Machine A, for example.
/Flibble
On 4/23/23 1:06 PM, Mr Flibble wrote:
On 23/04/2023 5:44 pm, Richard Damon wrote:
On 4/23/23 8:47 AM, Mr Flibble wrote:
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that >>>>>>>>>>>> forks the
simulation into two branches if the input calls the halt >>>>>>>>>>>> decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>>>>> }
When the simulator detects the call to H in P it forks the >>>>>>>>>>>> simulation
into a non-halting branch (returning 0 to P) and a halting >>>>>>>>>>>> branch
(returning 1 to P) and continues the simulation of these two >>>>>>>>>>>> branches
in parallel.
If the non-halting branch is determined to halt AND the >>>>>>>>>>>> halting branch
is determined to not halt then pathology is detected and >>>>>>>>>>>> reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE >>>>>>>>>>>> 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then >>>>>>>>>>>> that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>>>>> following case whereby the result of H is discarded by the >>>>>>>>>>>> input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a >>>>>>>>>>>> halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt. >>>>>>>>>>>> 3) Decider rejects pathological input as invalid by
signaling sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs >>>>>>>>>>>> which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered
definition of Halt Decoding.
It will decide that P() is pathological input and it will
decide that Px() is halting.
But those are just toy programs (P was just a simple program to >>>>>>>>> show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on >>>>>>>>> the following answers, its hard to see one.
You also need to clarify the rules of you computation system, >>>>>>>>>>> as you have previously commented that it can't obey the
"normal" rules used in computability theory.
I believe you are referring to the fact that the halt decider >>>>>>>>>> function and the intrinsic H(...) are a property of the
machine itself, H is much like the "move tape left" function >>>>>>>>>> of a Turing Machine. The only thing "abnormal" about it is >>>>>>>>>> that such a function is not included in the traditional
definition of a Turing Machine.
Your whole model of computation is at significant variance from >>>>>>>>> the classical theoretical model.
Also, how does your decider determine if the branch it is >>>>>>>>>>> following is non-halting.
The way any simulating halt decider would: through the
detection of repeated state given the machine and its
resources are finite in size.
So only able to detect non-halting in machines goig into
repeating loops, and not just that the computation keeps
growing unbounded.
Repeated state means a duplicate hash of the machine's finite
state.
But not suitable for things like the Twin Primes problem or
Collatz Conjecture.
Most of the interesting problems don't end up in a simple
infinite loop, but a loop counting through numbers that will
never reach there terminal condition.
>
The size of the set is relative. You are missing the point: to >>>>>>>> be computable the machine's resources can not be unbounded.
A very small set of the problems of normal interest in the theory. >>>>>>>>
Only problems that are computable using the technology of the
present era are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern
computer is unlikely to be the major limit. The "Very small set" >>>>>>> was the number of problems that can be handled, not the physical >>>>>>> size of the problems.
Remember, the problems that Halting was designed for were things >>>>>>> that a person with paper and pencil were trying to solve.
Detecting "simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly simple
issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i"
is of finite size so it will eventually wrap around to have the same
bit pattern a second time.
/Flibble
Depends on its type. It could be a big int (infinite precision
integer), so it runs until the machine exhausts its memory.
If you are admitting that you can only handle "finite" machines, then
that has been a solved problem for a long time. Even the pathological
program can be solved under finite memory limits (it will reach
memory exhaustion), which of course needs to be a fourth response
possible out of your decider.
Agree. As I posted earlier one has to be pragmatic given the finite
constraints: a halt decision may not be possible on Machine A but may
be possible on Machine B which has twice the resources of Machine A,
for example.
/Flibble
Yep, well known answer to the Halting Problem for fixed sized machines,
is a machine with (slightly more than) twice the memory needed for the program to decide, and run two copies of it, one at half speed.
You compare the memories of the machines, and if the algorithm gets in a
loop of length N, somewhere in 2N cycles of the faster machine, the two machines will line up and you will detect the repeated state.
On 23/04/2023 6:16 pm, Richard Damon wrote:
On 4/23/23 1:06 PM, Mr Flibble wrote:
On 23/04/2023 5:44 pm, Richard Damon wrote:
On 4/23/23 8:47 AM, Mr Flibble wrote:
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider that >>>>>>>>>>>>> forks the
simulation into two branches if the input calls the halt >>>>>>>>>>>>> decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop;
return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>>>>>> }
When the simulator detects the call to H in P it forks the >>>>>>>>>>>>> simulation
into a non-halting branch (returning 0 to P) and a halting >>>>>>>>>>>>> branch
(returning 1 to P) and continues the simulation of these >>>>>>>>>>>>> two branches
in parallel.
If the non-halting branch is determined to halt AND the >>>>>>>>>>>>> halting branch
is determined to not halt then pathology is detected and >>>>>>>>>>>>> reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE >>>>>>>>>>>>> 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided then >>>>>>>>>>>>> that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>>>>>> following case whereby the result of H is discarded by the >>>>>>>>>>>>> input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of >>>>>>>>>>>>> a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt. >>>>>>>>>>>>> 3) Decider rejects pathological input as invalid by
signaling sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs >>>>>>>>>>>>> which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered >>>>>>>>>>>> definition of Halt Decoding.
It will decide that P() is pathological input and it will >>>>>>>>>>> decide that Px() is halting.
But those are just toy programs (P was just a simple program >>>>>>>>>> to show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on >>>>>>>>>> the following answers, its hard to see one.
You also need to clarify the rules of you computation
system, as you have previously commented that it can't obey >>>>>>>>>>>> the "normal" rules used in computability theory.
I believe you are referring to the fact that the halt decider >>>>>>>>>>> function and the intrinsic H(...) are a property of the
machine itself, H is much like the "move tape left" function >>>>>>>>>>> of a Turing Machine. The only thing "abnormal" about it is >>>>>>>>>>> that such a function is not included in the traditional
definition of a Turing Machine.
Your whole model of computation is at significant variance >>>>>>>>>> from the classical theoretical model.
Also, how does your decider determine if the branch it is >>>>>>>>>>>> following is non-halting.
The way any simulating halt decider would: through the
detection of repeated state given the machine and its
resources are finite in size.
So only able to detect non-halting in machines goig into
repeating loops, and not just that the computation keeps
growing unbounded.
Repeated state means a duplicate hash of the machine's finite >>>>>>>>> state.
But not suitable for things like the Twin Primes problem or
Collatz Conjecture.
Most of the interesting problems don't end up in a simple
infinite loop, but a loop counting through numbers that will
never reach there terminal condition.
>
A very small set of the problems of normal interest in the >>>>>>>>>> theory.
The size of the set is relative. You are missing the point: to >>>>>>>>> be computable the machine's resources can not be unbounded.
Only problems that are computable using the technology of the >>>>>>>>> present era are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern
computer is unlikely to be the major limit. The "Very small set" >>>>>>>> was the number of problems that can be handled, not the physical >>>>>>>> size of the problems.
Remember, the problems that Halting was designed for were things >>>>>>>> that a person with paper and pencil were trying to solve.
Detecting "simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly
simple issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i"
is of finite size so it will eventually wrap around to have the
same bit pattern a second time.
/Flibble
Depends on its type. It could be a big int (infinite precision
integer), so it runs until the machine exhausts its memory.
If you are admitting that you can only handle "finite" machines,
then that has been a solved problem for a long time. Even the
pathological program can be solved under finite memory limits (it
will reach memory exhaustion), which of course needs to be a fourth
response possible out of your decider.
Agree. As I posted earlier one has to be pragmatic given the finite
constraints: a halt decision may not be possible on Machine A but may
be possible on Machine B which has twice the resources of Machine A,
for example.
/Flibble
Yep, well known answer to the Halting Problem for fixed sized
machines, is a machine with (slightly more than) twice the memory
needed for the program to decide, and run two copies of it, one at
half speed.
You compare the memories of the machines, and if the algorithm gets in
a loop of length N, somewhere in 2N cycles of the faster machine, the
two machines will line up and you will detect the repeated state.
Yes, that sounds like a good solution and is what I would do if I was to actually implement the Flibble SSHD.
/Flibble
On 4/23/23 4:28 PM, Mr Flibble wrote:
On 23/04/2023 6:16 pm, Richard Damon wrote:
On 4/23/23 1:06 PM, Mr Flibble wrote:
On 23/04/2023 5:44 pm, Richard Damon wrote:
On 4/23/23 8:47 AM, Mr Flibble wrote:
On 23/04/2023 12:27 pm, Richard Damon wrote:
On 4/22/23 11:47 PM, Mr Flibble wrote:
On 23/04/2023 3:42 am, Richard Damon wrote:
On 4/22/23 9:55 PM, Mr Flibble wrote:
On 23/04/2023 1:39 am, Richard Damon wrote:
On 4/22/23 8:31 PM, Mr Flibble wrote:
On 23/04/2023 12:53 am, Richard Damon wrote:
On 4/22/23 7:43 PM, Mr Flibble wrote:
Hi!
I have an idea for a signaling simulating halt decider >>>>>>>>>>>>>> that forks the
simulation into two branches if the input calls the halt >>>>>>>>>>>>>> decider as
per [Strachey 1965]'s "Impossible Program":
void P(void (*x)())
{
if (H(x, x))
infinite_loop: goto infinite_loop; >>>>>>>>>>>>>> return;
}
int main()
{
std::cout << "Input halts: " << H(P, P) << std::endl; >>>>>>>>>>>>>> }
When the simulator detects the call to H in P it forks the >>>>>>>>>>>>>> simulation
into a non-halting branch (returning 0 to P) and a halting >>>>>>>>>>>>>> branch
(returning 1 to P) and continues the simulation of these >>>>>>>>>>>>>> two branches
in parallel.
If the non-halting branch is determined to halt AND the >>>>>>>>>>>>>> halting branch
is determined to not halt then pathology is detected and >>>>>>>>>>>>>> reported via
a sNaP (signaling Not a Program) signal (analogous to IEEE >>>>>>>>>>>>>> 754's
sNaN (signaling Not a Number) signal)
If EITHER branch is determined to be correctly decided >>>>>>>>>>>>>> then that will
be the decision of the halting decider.
Crucially this scheme will handle (and correctly decide) the >>>>>>>>>>>>>> following case whereby the result of H is discarded by the >>>>>>>>>>>>>> input:
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of >>>>>>>>>>>>>> a halt
decider:
1) Decider decision is HALTS if input halts.
2) Decider decision is NON-HALTING if input does not halt. >>>>>>>>>>>>>> 3) Decider rejects pathological input as invalid by >>>>>>>>>>>>>> signaling sNaP.
Thoughts? I am probably missing something obvious as my idea >>>>>>>>>>>>>> appears to refute [Strachey 1965] and associated HP proofs >>>>>>>>>>>>>> which
great minds have mulled over for decades.
/Flibble
So, see if you can show an actual use for your altered >>>>>>>>>>>>> definition of Halt Decoding.
It will decide that P() is pathological input and it will >>>>>>>>>>>> decide that Px() is halting.
But those are just toy programs (P was just a simple program >>>>>>>>>>> to show classical halting to not be useful)
What USEFUL resutls can be gotten with your decider. Based on >>>>>>>>>>> the following answers, its hard to see one.
You also need to clarify the rules of you computation >>>>>>>>>>>>> system, as you have previously commented that it can't obey >>>>>>>>>>>>> the "normal" rules used in computability theory.
I believe you are referring to the fact that the halt
decider function and the intrinsic H(...) are a property of >>>>>>>>>>>> the machine itself, H is much like the "move tape left" >>>>>>>>>>>> function of a Turing Machine. The only thing "abnormal" >>>>>>>>>>>> about it is that such a function is not included in the >>>>>>>>>>>> traditional definition of a Turing Machine.
Your whole model of computation is at significant variance >>>>>>>>>>> from the classical theoretical model.
Also, how does your decider determine if the branch it is >>>>>>>>>>>>> following is non-halting.
The way any simulating halt decider would: through the >>>>>>>>>>>> detection of repeated state given the machine and its
resources are finite in size.
So only able to detect non-halting in machines goig into >>>>>>>>>>> repeating loops, and not just that the computation keeps >>>>>>>>>>> growing unbounded.
Repeated state means a duplicate hash of the machine's finite >>>>>>>>>> state.
But not suitable for things like the Twin Primes problem or
Collatz Conjecture.
Most of the interesting problems don't end up in a simple
infinite loop, but a loop counting through numbers that will >>>>>>>>> never reach there terminal condition.
>
A very small set of the problems of normal interest in the >>>>>>>>>>> theory.
The size of the set is relative. You are missing the point: >>>>>>>>>> to be computable the machine's resources can not be unbounded. >>>>>>>>>> Only problems that are computable using the technology of the >>>>>>>>>> present era are of interest: one has to be a pragmatist.
/Flibble
For many of the problems, the "limited" memory of the modern >>>>>>>>> computer is unlikely to be the major limit. The "Very small
set" was the number of problems that can be handled, not the >>>>>>>>> physical size of the problems.
Remember, the problems that Halting was designed for were
things that a person with paper and pencil were trying to
solve. Detecting "simple" loops wasn't the problem.
I am not sure why you are equating repeated finite state with
"simple" loops.
/Flibble
Because your "repeated state" method won't catch even fairly
simple issues like:
for(i = 100; i != 1; i -= 2;) {
// do something but don't change i
}
because the "state" never repeats
Of course that state repeats (and will be caught): the integer "i" >>>>>> is of finite size so it will eventually wrap around to have the
same bit pattern a second time.
/Flibble
Depends on its type. It could be a big int (infinite precision
integer), so it runs until the machine exhausts its memory.
If you are admitting that you can only handle "finite" machines,
then that has been a solved problem for a long time. Even the
pathological program can be solved under finite memory limits (it
will reach memory exhaustion), which of course needs to be a fourth
response possible out of your decider.
Agree. As I posted earlier one has to be pragmatic given the finite
constraints: a halt decision may not be possible on Machine A but
may be possible on Machine B which has twice the resources of
Machine A, for example.
/Flibble
Yep, well known answer to the Halting Problem for fixed sized
machines, is a machine with (slightly more than) twice the memory
needed for the program to decide, and run two copies of it, one at
half speed.
You compare the memories of the machines, and if the algorithm gets
in a loop of length N, somewhere in 2N cycles of the faster machine,
the two machines will line up and you will detect the repeated state.
Yes, that sounds like a good solution and is what I would do if I was
to actually implement the Flibble SSHD.
/Flibble
But that never generates your NaP exception, and never needs to, so the Flibble SSHD is shown to not be needed at all.
The problem space being solved by it was already solved.
Once you limit yourself to memory limited machines, the Halt Decider
just needs to make sure that the "pathological" programs die of
out-of-memory errors.
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