novaBBS - comp.theory - Re: Alan Turing's Halting Problem is incorrectly formed [my first post back in 2004]

Re: Alan Turing's Halting Problem is incorrectly formed [my first post back in 2004]

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by: olcott - Sat, 18 Mar 2023 16:51 UTC

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 2023 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Re: Alan Turing's Halting Problem is incorrectly formed [my first post back in 2004]

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by: Richard Damon - Sat, 18 Mar 2023 19:06 UTC

On 3/18/23 12:51 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)
>>    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.
>>
>>
>>
>

And how does an machine neither Halt or Run Forever?

Information is the inverse of entropy.

devel / comp.theory / Re: Alan Turing's Halting Problem is incorrectly formed [my first post back in 2004]

Subject	Author
Alan Turing's Halting Problem is incorrectly formed [my first	olcott
Alan Turing's Halting Problem is incorrectly formed [my first	Richard Damon