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

On 5/11/2025 10:03 PM, olcott wrote:

On 5/11/2025 8:31 PM, Richard Damon wrote:

On 5/11/25 8:29 PM, olcott wrote:

On 5/11/2025 6:39 PM, Richard Damon wrote:

On 5/11/25 5:15 PM, olcott wrote:

On 5/11/2025 4:02 PM, Richard Damon wrote:

On 5/11/25 12:44 PM, olcott wrote:

On 5/11/2025 6:13 AM, joes wrote:

Am Sat, 10 May 2025 15:42:13 -0500 schrieb olcott:

On 5/10/2025 3:22 PM, Alan Mackenzie wrote:

>

OK, then, give the page and line numbers from Turing's 1936 paper where
this alleged mistake was made.  I would be surprised indeed if you'd
even looked at Turing's paper, far less understood it.  Yet you're
ready to denigrate his work.
Perhaps it is time for you to withdraw these uncalled for insinuations.
>

It is the whole gist of the entire idea of the halting problem proof
that is wrongheaded.
(1) It is anchored in the false assumption that an input to a
termination analyzer can actually do this opposite of whatever value
that this analyzer returns. No one ever notices that this "do the
opposite" code is unreachable.

>

The simulated DDD doesn't matter. HHH returns to DDD, and DDD then does
the opposite.
>

>
HHH is only allowed to report on the behavior that
its actual input actually specifies.

>
>
Which is DEFINED to be the bahavior of the program that the input represents when run.

>
When you define 5 == 6 you are simply wrong.
That definition contradicts other axioms.
>

>
And where did I do that?
>

>
When the definition of the halting problem requires
the termination analyzer H to report on behavior besides
the behavior of the input D simulated by H according
to the rules of the computational language that the
input D is encoded within.
>

>
Where do you get that behavior to be decided needs to be based on the partial simulation of the decider.
>

 The behavior of the input to HHH(DDD) is only correctly
measured by

The algorithm that DDD describes, as that is what we want to know about:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly