Re: HHH decides a non-trivial semantic property of its input

On 2024-08-07 13:23:54 +0000, olcott said:

On 8/7/2024 2:06 AM, Mikko wrote:

On 2024-08-05 13:46:11 +0000, olcott said:
 

On 8/5/2024 8:44 AM, Python wrote:

Le 05/08/2024 à 13:50, olcott a écrit :

On 8/5/2024 3:08 AM, Mikko wrote:

On 2024-08-04 14:46:02 +0000, olcott said:
 

When we define an input that does the opposite of whatever
value that its halt decider reports there is a way for the
halt decider to report correctly.
 int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
 int main()
{
   HHH(DD);
}
 HHH returns false indicating that it cannot
correctly determine that its input halts.
True would mean that its input halts.

 That is called a "partial halt decider". The set of requirements is
a subset of the requirements for "halt decider" but still require
that the answer is not "halts" if the input does not halt and that
the answer is not "does not halt" if the input halts. The difference
is that a "halt decider" is required to give one of these answers
for every input but a "partial halt decider" is not.
 For every computation there is a partial halt decider that answers it.
 

 I call it a halting decidability decider.
1=input halts
0=input does not halt or has pathological relationship with its decider

 So it is NOT an halt decider. Case closed. You've lost your time
for years, and made a lot of people lose their time too.
  

 It refutes Rice

 No, it does not. Nothing is refuted as long as you have not proven anything.
 

 1 = halts = good input = decidable
0 = (not halts or pathological) = bad input = not decidable as halting
HHH decides a non-trivial semantic property of its input.

Your "not decidable as halting" is not a property of input. Another
partial decider may be able to determine that the input is halting
and therefore decidable as halting.
--
Mikko