Re: Hypothetical possibilities

On 2024-07-22 15:05:41 +0000, olcott said:

On 7/22/2024 6:05 AM, Mikko wrote:

On 2024-07-20 15:28:31 +0000, olcott said:
 

void DDD()
{
   HHH(DDD);
}
 int main()
{
   DDD();
}
 (a) Termination Analyzers / Partial Halt Deciders must halt
this is a design requirement.

 For a partial analyzer or deciders this is not always required.
 

 *You can't even get my words correctly*
A termination analyzer must report on the behavior of at least
one input for all of the inputs of this one input. This is
met when a termination analyzer analyzes an input having no inputs.
 A partial halt decider must correctly determine the halt status
of at least one input and its specific input (if any).
 HHH is both a partial halt decider and a termination analyzer
for DDD and a few other inputs having no input.
 

(b) Every simulating termination analyzer HHH either
aborts the simulation of its input or not.

 This must be interpreted to mean that a simulating termination analyzer
may abort its simulation for some simulated abort and simulate others
to the termination.
 

 I am talking about hypothetical possible ways that HHH could be encoded.
(a) HHH(DDD) is encoded to abort its simulation.
(b) HHH(DDD) is encoded to never abort its simulation.
 

(c) Within the hypothetical case where HHH does not abort
the simulation of its input {HHH, emulated DDD and executed DDD}
never stop running.

 The case is not very hypothetical. Given the HHH you already have,
it is fairly easy to construct the "hypothetical" HHH and see what
it actually does.
 

 (a) HHH(DDD) is encoded to abort its simulation.
(b) HHH(DDD) is encoded to never abort its simulation.
 

This violates the design requirement of (a) therefore HHH must
abort the simulation of its input.

 The violation simply means that the "hypothetical" HHH is not a
termination analyzer of partial halt decider in sense (a). What
it "must" be or do depends on the requirements.
 

Therefore (a) is correct and (b) is incorrect according to the
design requirements for HHH that it must halt.
 It is also a truism that any input that must be aborted
is a non-halting input.

No, it is not. The "must" and "non-halting" belong to different worlds.
The word "must" blongs to requirements. The word "non-halting" is a
feature of a program. They are unrelated, so one cannot be inferred
from the other.
--
Mikko