Re: Can D simulated by H terminate normally?

On 2024-05-03 11:55:15 +0000, olcott said:

On 5/3/2024 4:33 AM, Mikko wrote:

On 2024-05-02 18:35:19 +0000, olcott said:
 

On 5/2/2024 4:39 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/30/2024 5:46 PM, Richard Damon wrote:

On 4/30/24 12:15 PM, olcott wrote:

On 4/30/2024 10:44 AM, Alan Mackenzie wrote:

olcott <polcott333@gmail.com> wrote:

On 4/30/2024 3:46 AM, Fred. Zwarts wrote:

Op 29.apr.2024 om 21:04 schreef olcott:

 [ .... ]
 

When we add the brand new idea of {simulating termination analyzer} to
the existing idea of TM's then we must be careful how we define halting
otherwise every infinite loop will be construed as halting.

 

Why?

 

That doesn't mean the machine reached a final state.

 

Alan seems to believe that a final state is whatever state that an
aborted simulation ends up in.

 Only through your twisted reasoning.  For your information, I hold to the
standard definition of final state, i.e. one which has no state following
it.  An aborted simulation is in some state, and that state is a final
one, since there is none following it.
 

On 4/30/2024 10:44 AM, Alan Mackenzie wrote:

You are thus mistaken in believing "abnormal" termination
isn't a final state.

 

Only if you try to define something that is NOT related to Halting, do
you get into that issue.

 

"The all new ideas are wrong" assessment.
Simulating termination analyzers <are> related to halting.

 Except you cannot define what such a thing is, and that relationship is
anything but clear.

 When a simulating termination analyzer matches one of three
non-halting behavior patterns
(a) Simple Infinite loop
(b) Simple Infinite Recursion
(c) Simple Recursive Simulation

 Simple recursive simulation is not a non-halting behaviour
if the recursion is not infinite.

 In other words the only way that we can tell that an infinite
loop never halts is to simulate it until the end of time?

The phrase "in other words" is not correct here as it means that
what follows means the same as what precedes, and that is not
true here.
For same loops the only wha to detect non-termination may be
to simulate to infinity but they can be considered exluded by
the term "simple" in (a).

There are repeating state non-halting behavior patterns
that can be recognized. These are three more functions
where H derives the correct halt status:
 void Infinite_Recursion(u32 N)
{
   Infinite_Recursion(N);
}

Per (b) that is non-halting and indeed it is (though the
execution may crash for "out of memeory").

void Infinite_Loop()
{
   HERE: goto HERE;
}

Per (a) that is non-halting and indeed it is.

int factorial(int n)
{
   if (n >= 1)
     return n*factorial(n-1);
   else
     return 1;
}

Per (c) that is non-halting but in reality it is not.
Ergo, the rule (c) is wrong.
--
Mikko