From Newsgroup: comp.lang.c

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)
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.

--
Copyright 2024 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer
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From Newsgroup: comp.lang.c

On 8/24/2025 4:56 PM, olcott wrote:

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.

https://www.usenetarchives.com/view.php?id=sci.logic&mid=PGJDRndjLjEzOTgwJEd4NC4yNTM3QGJndG5zYzA0LW5ld3Mub3BzLndvcmxkbmV0LmF0dC5uZXQ%2B
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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