Re: How the requirements that Professor Sipser agreed to are exactly met

On 5/12/2025 10:01 PM, olcott wrote:

On 5/12/2025 8:45 PM, dbush wrote:

On 5/12/2025 9:06 PM, olcott wrote:

On 5/12/2025 8:00 PM, dbush wrote:

On 5/12/2025 8:56 PM, olcott wrote:

On 5/12/2025 7:36 PM, dbush wrote:

On 5/12/2025 8:34 PM, olcott wrote:

On 5/12/2025 7:27 PM, dbush wrote:

On 5/12/2025 8:25 PM, olcott wrote:

On 5/12/2025 7:12 PM, dbush wrote:

On 5/12/2025 7:53 PM, olcott wrote:

>
Simulating Termination analyzers cannot possibly report
on the actual behavior of non-terminating inputs
because this would cause themselves to never terminate.
>
They must always hypothesize what the behavior of the
input would be if they themselves never aborted.
>

>
False.  They must always hypothesize what the behavior of algorithm described by the input would be if it was executed directly, as per the requirements:
>

>
Show the actual reasoning of how it makes sense
that a simulating termination analyzer should
ignore the behavior (to its own peril) that the
input actually specifies.

>
There is no requirement that building a termination analyzer, simulating or otherwise, is possible.  In fact, it has proved to not be possible by Linz and others, which you have *explicitly* agreed with.
>

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In other words you have no such actual reasoning.

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The reasoning is that there is no requirement that building a termination analyzer is possible.

>
So you have no actual reasoning that addresses my
actual point.
>
 >>>> Show the actual reasoning of how it makes sense
 >>>> that a simulating termination analyzer should
 >>>> ignore the behavior (to its own peril) that the
 >>>> input actually specifies.
>

>
It makes sense because that's what's required to tell me if any arbitrary algorithm X with input Y will halt when executed directly.
>

>
Exactly what actual reasoning shows that this
is superior to reporting on the behavior that
its input actual specifies?

>
I'll let you respond to yourself:
>
On 7/30/2024 10:21 AM, olcott wrote:
 > *Its all in the part that you erased*
>
On 11/12/2024 12:21 PM, olcott wrote:
 > *IT WAS DISHONEST THAT YOU ERASED THIS PART*
>
Which I have restored below:
>

Let the record show that there was no denying the dishonest behavior above.

>

It would be *very* useful to me if I had an algorithm H that could tell me that in *all* possible cases.  If so, I could solve the Goldbach conjecture and make unknownable truths knowable, among many other unsolved problems.
>

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And so I'll ask a second time:
>

Does an algorithm H exist that can tell me that or not?

>

 If the Goldbach conjecture is true (and there is
no short-cut) this requires testing against every
element of the set of natural numbers an infinite
computation.

And if we take that computation and feed it into an H that meets these requirements:
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
Then if H reports non-halting the Goldbach conjecture is true, and if H reports halting the Goldbach conjecture is false.
If on the other hand we feed the computation to an H that tells us if it "specifies non-halting behavior to H", we won't necessarily get that answer.  We have to worry about how the computation is implemented. With the above requirements we don't need to worry about that.
The same applies to *any* process which may or may not be infinite to tell us whether or not it is actually an infinite process.

 *That had nothing to do with this point*

False, see above.

  >> Exactly what actual reasoning shows that this
 >> is superior to reporting on the behavior that
 >> its input actual specifies?