Re: Hypothetical possibilities

Am Sat, 20 Jul 2024 15:05:53 -0500 schrieb olcott:

On 7/20/2024 2:50 PM, Richard Damon wrote:

On 7/20/24 3:09 PM, olcott wrote:

On 7/20/2024 2:00 PM, Fred. Zwarts wrote:

Op 20.jul.2024 om 17:28 schreef olcott:

(a) Termination Analyzers / Partial Halt Deciders must halt this is
a design requirement.
(b) Every simulating termination analyzer HHH either aborts the
simulation of its input or not.
(c) Within the hypothetical case where HHH does not abort the
simulation of its input {HHH, emulated DDD and executed DDD}
never stop running.
This violates the design requirement of (a) therefore HHH must abort
the simulation of its input.

You missed a couple details:
A terminating input shouldn't be aborted, or at least not classified
as not terminating. Terminating inputs needn't be aborted; they and the
simulator halt on their own.

And when it aborts, the simulation is incorrect. When HHH aborts and
halts, it is not needed to abort its simulation, because it will halt
of its own.

So you are trying to get away with saying that no HHH ever needs to
abort the simulation of its input and HHH will stop running?

Pretty much.

It is the fact that HHH DOES abort its simulation that makes it not
need to.

No stupid it is not a fact that every HHH that can possibly exist aborts
its simulation.

I thought they all halt after a finite number of steps?

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.