Re: H(D,D) cannot even be asked about the behavior of D(D)

On 6/15/24 9:24 AM, olcott wrote:

On 6/15/2024 7:33 AM, Mikko wrote:

On 2024-06-15 11:34:39 +0000, joes said:
>

Am Fri, 14 Jun 2024 12:39:15 -0500 schrieb olcott:

On 6/14/2024 10:54 AM, joes wrote:

Am Fri, 14 Jun 2024 08:15:52 -0500 schrieb olcott:

On 6/14/2024 6:39 AM, Richard Damon wrote:

On 6/14/24 12:13 AM, olcott wrote:

On 6/13/2024 10:44 PM, Richard Damon wrote:

On 6/13/24 11:14 PM, olcott wrote:

On 6/13/2024 10:04 PM, Richard Damon wrote:

On 6/13/24 9:39 PM, olcott wrote:

On 6/13/2024 8:24 PM, Richard Damon wrote:

On 6/13/24 11:32 AM, olcott wrote:

>

When H and D have a pathological relationship to each other then
H(D,D) is not being asked about the behavior of D(D). H1(D,D) has no
such pathological relationship thus D correctly simulated by H1 is the
behavior of D(D).

What is H1 asked?

H is asked whether its input halts, and by definition should give the
(right) answer for every input.

If we used that definition of decider then no human ever decided
anything because every human has made at least one mistake.

Yes. Humans are not machines.

I use the term "termination analyzer" as a close fit. The term partial
halt decider is more accurate yet confuses most people.

>
Olcott has used the term "termination analyzer", though whether he knows
what it means is unclear.
>

 To prove (non-)termination of a C program, AProVE uses the Clang compiler [7] to translate it to the intermediate representation of the LLVM framework [15]. Then AProVE symbolically executes the LLVM program and uses abstraction to obtain a finite symbolic execution graph (SEG) containing all possible program runs.
 *AProVE: Non-Termination Witnesses for C Programs*
https://link.springer.com/content/pdf/10.1007/978-3-030-99527-0_21.pdf
 

The main difference is that a halt decider or partial halt decider takes
descriptions of both a Turing machine (or other program) and an input and
determines whether that machine halts with that input

 H(D,D) is only required to get this one input correctly thus H is
a halt decider with a domain restricted to D.
 

And since it gets the one answer it is resposible for wrong, it fails.
Since H(D,D) returns 0, it can be proven that D(D) will halt, which *IS* the behavior a "Halt Decider" (even a limited halt decider) is responsible for answering about, so H(D,D) is just WRONG.

but a termination
analyzer takes only the dexcription of a Turing machine (or other program)
and attempts to determine whether that machine halts with every input.
The term "analyzer" instead "decider" indicates that it may fail to
determine on some inputs

 Yes that is the distinction that I intend.

But it fails on the one machine you want it to answer about.

 

and that it may produce additional information
that may be useful. The intent is to create termination analyzers that
are useful for practical purposes.
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