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

On 5/11/2025 6:30 PM, olcott wrote:

On 5/11/2025 5:11 PM, wij wrote:

On Sun, 2025-05-11 at 17:00 -0500, olcott wrote:
[cut]

ZFC corrected the error in set theory so that
it could resolve Russell's Paradox. The original
set theory has now called naive set theory.
>
I corrected the error of the HP that expects
HHH to report on behavior that is different
than the behavior that its input actually
specifies.

>
Specificly, "Halt(D)=1 iff D() halts" is an error?
And it should expect: Halt(D)=1 iff POOH(D)=1 (correct problem)?
>

>
Yes that is an error because the behavior that
the input to HHH(DDD) specifies is the behavior
that HHH must report on.

>
If so, how do we know a given function e.g. D, halts or not by giving it to H,
i.e. H(D)? Wrong question (according to you)?

 H and D is too vague and ambiguous.
We know that the input to HHH(DDD) specifies
a non-halting sequence of configurations.
 We know that the input to HHH1(DDD) specifies
a halting sequence of configurations.
 

Instead, every time we want to know whether D halts or not,

 When we intentionally define an input to attempt
to thwart a specific termination analyzer THIS DOES
CHANGE THE BEHAVIOR.
 If we let people run uploaded programs on our
network we need to know if these programs are
going to halt.

Which means it will give us the wrong answer for DDD, as it will halt when executed directly, which is what we want to know about.
Telling us that DDD "specifies non-halting behavior to HHH" is useless.