Re: The halting problem as defined is a category error

Am Wed, 23 Jul 2025 09:24:15 -0500 schrieb olcott:

On 7/23/2025 8:31 AM, joes wrote:

Am Wed, 23 Jul 2025 07:22:55 -0500 schrieb olcott:

On 7/23/2025 2:34 AM, Mikko wrote:

On 2025-07-22 13:56:36 +0000, olcott said:

The category error is the mistake of assuming that a directly
executing Turing machine is in the category of input to a Turing
machine halt decider.

>
That error is not present in the halting problem. It is also not
present in https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
which is the prototype of proofs that you falsely claim to have
refuted.
>

I am either going to go by the Linz proof or my own code

Your decision. Anyway the hypothetical halting decider obviously only
takes descriptions of TMs as input, with the OUTput required to be what
the universal simulation or direct execution *of that input* (namely,
DDD *not* calling a UTM) does.
 

That is incorrect in the case where DD calls its own simulating
termination analyzer or the Linz Ĥ contains its own simulating halt
decider.

Yes, HHH does not meet the requirement.

The actual behavior that is actually specified must include that in both
of these cases recursive simulation is specified. We can't just close
our eyes and pretend otherwise.

That is what HHH does: close its eyes and pretend that DDD called a
pure simulator instead of recursing. See below.

Then the word "speifies" needs a definition. The clearest formulation
is to ask about an Universal Turing machine. Then the input to the
decider is the same as the input tu the Universal Turing machine.

 

When an input calls its own decider in recursive emulation this must
be modeled. The best way to determine the behavior that the input
specifies is for DD to be emulated by HHH according to the semantics
of the x86 language. That does cause recursive emulation.

>
No, the best way to determine what the input "specifies" is to just run
it or use a UTM - unless you actually mean the behaviour of HHH
simulating DDD, in which case it is always tautologically correct.

You gotta say something about this.

--
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.