Re: Halting Problem: What Constitutes Pathological Input

On 5/7/2025 4:44 PM, olcott wrote:

On 5/7/2025 3:25 PM, joes wrote:

Am Tue, 06 May 2025 10:23:18 -0500 schrieb olcott:

On 5/6/2025 4:30 AM, Mikko wrote:

On 2025-05-05 19:27:18 +0000, olcott said:

On 5/5/2025 2:12 PM, dbush wrote:

On 5/5/2025 2:47 PM, olcott wrote:

On 5/5/2025 1:21 PM, dbush wrote:

On 5/5/2025 2:14 PM, olcott wrote:

On 5/5/2025 11:16 AM, dbush wrote:

On 5/5/2025 12:13 PM, Mr Flibble wrote:

On Mon, 05 May 2025 11:58:50 -0400, dbush wrote:

On 5/5/2025 11:51 AM, olcott wrote:

>
>

When HHH computes the mapping from *its input* to the behavior
of DD emulated by HHH this includes HHH emulating itself
emulating DD. This matches the infinite recursion behavior
pattern.
Thus the Halting Problem's "impossible" input is correctly
determined to be non-halting.
>

Which is a contradiction.  Therefore the assumption that the
above mapping is computable is proven false, as Linz and others
have proved and as you have *explicitly* agreed is correct.

>
The category (type) error manifests in all extant halting
problem proofs including Linz.  It is impossible to prove
something which is ill- formed in the first place.

>
All algorithms either halt or do not halt when executed directly.
Therefore the problem is not ill formed.
>

When BOTH Boolean RETURN VALUES are the wrong answer THEN THE
PROBLEM IS ILL-FORMED. Self-contradiction must be screened out as
semantically incorrect.

>
In other words, you're claiming that there exists an algorithm,
i.e. a fixed immutable sequence of instructions, that neither halts
nor does not halt when executed directly.
>

That is not what I said.

>
Then there's no category error, and the halting function is well
defined.  It's just that no algorithm can compute it.

>
It is insufficiently defined thus causing it to be incoherently
defined.

>
It is well defined. There are computations that halt and computations
that do not. Nothing else is in the scope of the halting problem.
>

It is incorrectly defined when-so-ever it is not specified that a
specific sequence of steps must be applied to the input to derive the
output.
That DD() halts therefore I guess that DD correctly emulated by HHH must
halt too IS NOT A SPECIFIC SEQUENCE OF STEPS.
It is merely an incorrect guess.

 

Oh wow. As a simulator, HHH must produce the same behaviour as the direct
execution.
>

 If you examine 100% of ALL of the details
you will find that is counter-factual.
 

Another lie, as you have admitted on the record that HHH and an actual correct simulation are the same up to the abort:
On 5/6/2025 5:17 PM, dbush wrote:
 > On 5/6/2025 5:03 PM, olcott wrote:
 >> On 5/6/2025 3:51 PM, dbush wrote:
 >>> On 5/6/2025 4:46 PM, olcott wrote:
 >>>> On 5/6/2025 3:31 PM, dbush wrote:
 >>>>> Then what is the first instruction emulated by HHH that differs
 >>>>> from the emulation performed by UTM?
 >>>>>
 >>>>
 >>>> HHH1 is exactly the same as HHH except that DD
 >>>> does not call HHH1. This IS the UTM emulator.
 >>>> It does not abort.
 >>>
 >>> Last chance:
 >>>
 >>> What is the first instruction emulated by HHH that differs from the
 >>> emulation performed by HHH1?
 >>
 >> Go back and read the part you ignored moron.
 >
 > Let the record show that Peter Olcott has neglected to identify an
 > instruction that HHH emulates differently from HHH1.
 >
 >>> Failure to provide this in your next message or within one hour of
 >>> your next post in this newsgroup will be taken as your official on-
 >>> the-record admission that the emulations performed by HHH and HHH1
 >>> are in fact exactly the same up until the point that HHH aborts, at
 >>> which point HHH did not correctly simulate the last instruction it
 >>> simulated as you are previously on record as admitting.
 >
 > Therefore, as per the above requirements:
 >
 > LET THE RECORD SHOW
 >
 > That Peter Olcott
 >
 > Has *officially* admitted
 >
 > That the emulations performed by HHH and HHH1 are in fact exactly the
 > same up until the point that HHH aborts, at which point HHH did not
 > correctly simulate the last instruction it simulated as he is previously
 > on record as admitting.