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One very simple transformation of the problem into a solvable problem
is to convert the Boolean function DoesItHalt() into a tertiary response: True, False, Neither.
if (DoesItHalt() == True)
while(True) // loop forever
;
else if (DoesItHalt() == False)
return False;
else if (DoesItHalt() == NeitherTrueNorFalse)
return NeitherTrueNorFalse;
So the original Halting Problem was incorrectly formed specifically
because it was framed as a Boolean function, thus failing to account
for possible inputs that result in a reply other than True or False.
On 6/6/2004 9:11 AM, Peter Olcott wrote:
One very simple transformation of the problem into a solvable problem
is to convert the Boolean function DoesItHalt() into a tertiary response:
True, False, Neither.
if (DoesItHalt() == True)
-a-a while(True)-a-a // loop forever
-a-a-a-a ;
else if (DoesItHalt() == False)
-a-a return False;
else if-a (DoesItHalt() == NeitherTrueNorFalse)
-a-a return NeitherTrueNorFalse;
So the original Halting Problem was incorrectly formed specifically
because it was framed as a Boolean function, thus failing to account
for possible inputs that result in a reply other than True or False.