Philosophy of Computation: Three seem to agree how emulating termination analyzers are supposed to work

*The best selling author of theory of computation textbooks*
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
If simulating halt decider H correctly simulates its input D
until H correctly determines that its simulated D would never
stop running unless aborted then
H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
Correct simulation is defined as D is emulated by H according to
the semantics of the x86 language thus includes H emulating itself
emulating D.
I made D simpler so that the key essence of recursive simulation
could be analyzed separately. ChatGPT totally understood this.
void DDD()
{
HHH(DDD);
return;
}
ChatGPT
Simplified Analogy:
Think of HHH as a "watchdog" that steps in during real execution
to stop DDD() from running forever. But when HHH simulates DDD(),
it's analyzing an "idealized" version of DDD() where nothing stops the
recursion. In the simulation, DDD() is seen as endlessly recursive, so
HHH concludes that it would not halt without external intervention.
https://chatgpt.com/share/67158ec6-3398-8011-98d1-41198baa29f2
This link is live so you can try to convince ChatGPT that its wrong.
On 11/3/2024 12:20 PM, Richard Damon wrote:
 > On 11/3/24 9:39 AM, olcott wrote:
 >>
 >> The finite string input to HHH specifies that HHH
 >> MUST EMULATE ITSELF emulating DDD.
 >
 > Right, and it must CORRECTLY determine what an unbounded
 > emulation of that input would do, even if its own programming
 > only lets it emulate a part of that.
 >
*Breaking that down into its key element*
 > [This bounded HHH] must CORRECTLY determine what
 > an unbounded emulation of that input would do...
When that input is unbounded that means it is never
aborted at any level, otherwise it is bounded at some
level thus not unbounded.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer