Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
Re: Halting Problem Final Conclusion (more than 16 years later)
5 views
Skip to first unread message
olcott
Jan 11, 2021, 2:05:03 PM1/11/21
to
On 9/5/2004 11:21 AM, Peter Olcott wrote:
> The Liar Paradox can be shown to be nothing more than
> a incorrectly formed statement because of its pathological
> self-reference. The Halting Problem can only exist because
> of this same sort of pathological self-reference.
>
> The primary benefit of solving the Halting Problem was to
> detect programs that failed to halt, thus were incorrect.
> Pathological self-reference can also be viewed as a form
> of error. If the Halting Problem is redefined (which does not
> refute anyone), then this redefined problem can be easily
> solved.
>
> Now we have three possible correct results:
> (a) Halts
> (b) Does Not Halt
> (c) Pathological Self Reference to Halt
>
> Compared to my prior claims, this one seem trivial and
> obvious. Possibly this claim adds a slight nuance to the
> problem that has not been widely discussed before.
> If we construe pathological self-reference as another
> error condition, then this does remove the impossibility
> of creating a useful tool.
>
>
The conventional halting problem undecidability proofs conclude that no
universal halt decider can possibly exist on the basis that a particular
class of universal halt deciders cannot possibly exist.
It seems to be true that no universal halt decider exists that attempts
to divide all of its inputs into halting and not halting on the basis of
answering the question:
Does the input program halt on its input?
On the other hand: A universal halt decider that attempts to divide all
of its inputs into halting and not halting on the basis of answering the
question:
Does the simulation of the input have to be stopped to prevent its
otherwise infinite execution?
Does not suffer from the Pathological self-reference(Olcott 2004) and
can thus be defined.
Because this revised criteria does divide its inputs into halting and
non-halting by this criteria:
On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
> A computation that would not halt if its simulation were not
> halted is indeed a non-halting computation.
On Saturday, November 28, 2020 at 2:00:28 PM UTC-8, olcott wrote:
> Every computation that would not halt if its simulation
> were not halted is by logical necessity a non-halting computation.
it still directly applies to the actual halting problem itself:
The Halting problem is a problem in computer science. The problem is
looking at a computer program and finding out if the program is going to
run forever or not. We say that a program "solves the halting problem"
if it can look at any other program and tell if that other program will
run forever or not.
https://simple.wikipedia.org/wiki/Halting_problem
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
> The Liar Paradox can be shown to be nothing more than
> a incorrectly formed statement because of its pathological
> self-reference. The Halting Problem can only exist because
> of this same sort of pathological self-reference.
>
> The primary benefit of solving the Halting Problem was to
> detect programs that failed to halt, thus were incorrect.
> Pathological self-reference can also be viewed as a form
> of error. If the Halting Problem is redefined (which does not
> refute anyone), then this redefined problem can be easily
> solved.
>
> Now we have three possible correct results:
> (a) Halts
> (b) Does Not Halt
> (c) Pathological Self Reference to Halt
>
> Compared to my prior claims, this one seem trivial and
> obvious. Possibly this claim adds a slight nuance to the
> problem that has not been widely discussed before.
> If we construe pathological self-reference as another
> error condition, then this does remove the impossibility
> of creating a useful tool.
>
>
The conventional halting problem undecidability proofs conclude that no
universal halt decider can possibly exist on the basis that a particular
class of universal halt deciders cannot possibly exist.
It seems to be true that no universal halt decider exists that attempts
to divide all of its inputs into halting and not halting on the basis of
answering the question:
Does the input program halt on its input?
On the other hand: A universal halt decider that attempts to divide all
of its inputs into halting and not halting on the basis of answering the
question:
Does the simulation of the input have to be stopped to prevent its
otherwise infinite execution?
Does not suffer from the Pathological self-reference(Olcott 2004) and
can thus be defined.
Because this revised criteria does divide its inputs into halting and
non-halting by this criteria:
On 11/27/2020 9:02 PM, Ben Bacarisse wrote:
> A computation that would not halt if its simulation were not
> halted is indeed a non-halting computation.
On Saturday, November 28, 2020 at 2:00:28 PM UTC-8, olcott wrote:
> Every computation that would not halt if its simulation
> were not halted is by logical necessity a non-halting computation.
it still directly applies to the actual halting problem itself:
The Halting problem is a problem in computer science. The problem is
looking at a computer program and finding out if the program is going to
run forever or not. We say that a program "solves the halting problem"
if it can look at any other program and tell if that other program will
run forever or not.
https://simple.wikipedia.org/wiki/Halting_problem
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
0 new messages