Re: Incorrect requirements --- Computing the mapping from the input to HHH(DD)

On 5/16/25 11:50 AM, olcott wrote:

On 5/16/2025 10:38 AM, joes wrote:

Am Sun, 11 May 2025 19:51:27 -0500 schrieb olcott:
>

If on a real system an input tried to fool the denial-of-service-attack
detector IT WOULD FAIL.
Prior to my work a denial-of-service-attack detector WOULD FAIL. It
would not know to reject DDD.

No, the goal is not to make HHH run forever. It would not fail at
terminating contrary to HHH's result.
>

 The goal of the counter-example input to the HP
proofs has always been to make halting undecidable
on this input. A simulating termination analyzer
fixes that.
 

No, it is to show that there is an input that this decider gets wrong.
"inputs" are not undecidable.
Problems are undecidable.
Which means there is not a single program that can give the correct answer to all instances of the problem.
The Halting Problem is undecidable, as there is no single decider "H", that can correct decide for all inputs, as for any SPECIFIC H, we can make a SPECIFIC D, based on that H, that it will get wrong.
H is not "an infinite set of deciders" as that isn't the right category.
H is a specific decider out of that infinite set of programs.
D is also, a specific input, different for each H chosen, which is why the proof calls it H^, to show that it is the input based on the ^ transform of H.
If you take a different decider HH, then we give it HH^, not H^, there is no reason HH can't correctly decide on H^ (it might or it might not, but the ^ transform doesn't assert anything about it).
The Simulating Halting Decider can't fix that, and be a program, as the proof didn't care about how the decider worked. Your attempts at trying to weasle word around things just shows you think it is ok to lie about what you are talking about, meaning nothing you say can be taken as truthful, as that is just a foreign concept to you.