Re: A Possible "solution" to the Halting Problem


"Paul E. Black" <p.black@xxxxxxx> wrote in message
news:eh5k9g02mma@xxxxxxxxxxxxxxxxxxxx
On Tuesday 17 October 2006 14:36, Peter Olcott wrote:
My primary point is based on the subtle distinction between your precise
statement of the conclusions that can be drawn from the HP, and the actual
correct conclusions that can actually be drawn. ...

The HP does not show any limitation what-so-ever to the capability to
determine the halting status of any program. All that the HP shows ...

In my personal experience I find that the unsolvability of the Halting
Problem is a real limit (not just a problem in, say, definition) and
that the theorem is useful.

From time to time we would have trouble "writing" some powerful
routines. We would think we had a solution, only to find we
overlooked something, and we'd try to generalize to solve the
*real* problem. Not infrequently after the second or third attempt,
we'd ponder and realize that the problem was equivalent to solving the
Halting Problem. With that we were satisfied with heuristics.

Because of these experiences and the proofs I've seen, I am skeptical
of purported solutions to the Halting Problem. True, the Halting
Problem may be redefined such that there is a solution, but I've never
found the redefined problem applicable in the real world.

Sincerely,
-paul-
--
Paul E. Black (p.black@xxxxxxx)

The conclusion of the Halting Problem is that it purports to show that some
things are not computable. If one treats English as a mathematical formalism,
one sees that this conclusion is flatly incorrect. The Halting problem does not
show that the correct halting status of every element in the set of all programs
can not be determined.

int WillHalt(string SourceCode, string InputData) {
if (MalignantSelfReference(SourceCode, InputData))
throw(MALIGNANT_SELF_REFERENCE);
if ( TheProgramWillHalt(SourceCode, InputData) )
return TRUE;
else
return FALSE;
}

This function breaks out of the infinite recursive self reference of the HP
thus defeating the conclusions drawn from the HP. It knows whether or not the
program under test halts, Since it KNOWS this therefore it HAS DETERMINED THIS.


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