Re: DDD simulated by HHH cannot possibly halt (Halting Problem) --- mindless robots

On 4/14/2025 4:29 AM, joes wrote:

Am Sun, 13 Apr 2025 16:00:43 -0500 schrieb olcott:

On 4/13/2025 3:00 PM, dbush wrote:

On 4/13/2025 3:59 PM, olcott wrote:

On 4/13/2025 3:54 AM, joes wrote:

Am Fri, 11 Apr 2025 10:56:32 -0500 schrieb olcott:

On 4/11/2025 3:24 AM, Richard Heathfield wrote:

On 11/04/2025 08:57, Mikko wrote:

>

No proof of this principle has been shown so its use is not
valid.

No proof of Peano's axioms or Euclid's fifth postulate has been
shown.
That doesn't mean we can't use them.
Mr Olcott can have his principle if he likes, but only by EITHER
proving it (which, as you say, he has not yet done) OR by taking
it as axiomatic, leaving the world of mainstream computer science
behind him,
constructing his own computational 'geometry' so to speak, and
abandoning any claim to having overturned the Halting Problem.
Navel contemplation beckons.
Axioms are all very well, and he's free to invent as many as he
wishes,
but nobody else is obliged to accept them.

*Simulating termination analyzer Principle*
It is always correct for any simulating termination analyzer to
stop simulating and reject any input that would otherwise prevent
its own termination.

Sure. Why doesn’t the STA simulate itself rejecting its input?

Because that is a STUPID idea and categorically impossible because
the outermost HHH sees its needs to stop simulating before any inner
HHH can possibly see this.

In other words, you agree that Linz and others are correct that no H
exists that satisfies 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

No stupid! Those freaking requirements are wrong and anchored in the
ignorance  of rejecting the notion of a simulating termination
analyzer OUT-OF-HAND WITHOUT REVIEW.
As anyone can see HHH MUST REJECT ITS INPUT OR GET STUPIDLY STUCK IN
NON-TERMINATION. If people were not mindless robots they would have
immediately acknowledged this years ago.

But why does it not return „I know this halts, but I can’t simulate
it”?

Because it is not a liar and tells the truth for every input in its
domain.