On 23/04/2023 10:23 pm, Richard Damon wrote:
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.
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.
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.
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.
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
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