Halting Problem solved!

Post by Mr Flibble
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
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
void Px(void (*x)())
{
    (void) H(x, x);
    return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Mr Flibble

2023-04-23 00:31:20 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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

olcott

2023-04-23 00:37:38 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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

You got the essence of that most important part correctly.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Richard Damon

2023-04-23 00:39:16 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Your whole model of computation is at significant variance from the
classical theoretical model.

Post by Richard Damon
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.

Post by Mr Flibble
/Flibble

Mr Flibble

2023-04-23 01:55:49 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.

Post by Richard Damon
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

Richard Damon

2023-04-23 02:42:47 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.

Post by Richard Damon
A very small set of the problems of normal interest in the theory.

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.

Mr Flibble

2023-04-23 03:47:06 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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

Richard Damon

2023-04-23 11:27:51 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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

Mr Flibble

2023-04-23 12:47:58 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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

Richard Damon

2023-04-23 16:44:07 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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.

Mr Flibble

2023-04-23 17:06:13 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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

Richard Damon

2023-04-23 17:16:47 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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.

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.

Mr Flibble

2023-04-23 20:28:07 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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

Richard Damon

2023-04-23 21:23:35 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
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
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.

Mr Flibble

2023-04-23 22:26:08 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
A very small set of the problems of normal interest in the theory.

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
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.

No, the pathological program of [Strachey 1965] still needs to be
explicitly detected as it won't die of an out-of-memory error: the so
called "infinite recursion" of Olcott's decider is a mistake.

/Flibble

olcott

2023-04-23 23:30:22 UTC

Post by Mr Flibble
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
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
void Px(void (*x)())
{
     (void) H(x, x);
     return;
}
Obviously my idea necessitates extending the definition
of a halt
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.

Post by Richard Damon
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.

Post by Richard Damon
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.
>

Post by Richard Damon
A very small set of the problems of normal interest in the theory.

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
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.

My C/x86 program is hypothesized to be a proxy for the behavior of an
equivalent Turing machine.

The idea was to understand the algorithm from the concrete X/x86 example
and then apply the same reasoning to the Peter Linz Turing Machine based
proof.

My new paper reverses the order of this because so many people rejected
the C/x86 out-of-hand as inapplicable to Turing Machines.

*Simulating (partial) Halt Deciders Defeat the Halting Problem Proofs*
https://www.researchgate.net/publication/369971402_Simulating_partial_Halt_Deciders_Defeat_the_Halting_Problem_Proofs

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Postiljon Petskin

2023-04-23 05:05:19 UTC

You know how stupid You look ? It is absolutely beyond belief !!!!!!!!!!!!!!!

Post by Mr Flibble
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
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
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
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.

Angle

2023-04-23 10:40:05 UTC

Hello....... You're not acting good.................

Post by Mr Flibble
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
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
void Px(void (*x)())
{
(void) H(x, x);
return;
}
Obviously my idea necessitates extending the definition of a halt
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

markus...@gmail.com

2024-02-20 20:33:52 UTC