Re: Functions computed by Turing Machines MUST apply finite string transformations to inputs --- MT

Am Sat, 03 May 2025 10:52:35 -0500 schrieb olcott:

On 5/2/2025 8:16 PM, Mike Terry wrote:

On 02/05/2025 06:06, Richard Heathfield wrote:

On 02/05/2025 05:08, dbush wrote:

On 5/1/2025 11:57 PM, olcott wrote:

On 5/1/2025 9:40 PM, dbush wrote:

So you changed the input.  Changing the input is not allowed.

I never changed the input.

Yes you did.  You hypothesize changing the code of HHH, and HHH is
part of the input. So you changed the input.

Agreed.

Still true.

Of course, Mr Olcott's change is rather different, because by changing
his HHH he's actually changing the behaviour of his DD - i.e.
specifying a new U - but I see no reason why he can't do that /
provided/ he can show that he always gets the correct answer. He has
so far failed to do this with the original HHH, and now he has doubled
his workload by giving himself another HHH to defend.

 
Right - PO's H is free to rewrite the tape in whatever way it likes,
provided in the end it gets the right answer.
The "you're not allowed to change the input" charge means something
quite different.
TLDR:  Your talking about TMs writing to their tape as part of their
normal operation.  Nothing wrong with that.  PO is effectively talking
about changing the meaning of D [the input to H] half way through the
Sipser quote.
 
 

-----------------------------------------------------------------------------

NTLFM:
PO is trying to interpret Sipser's quote:
--- Start Sipser quote
--- End Sipser quote
 
The following interpretation is ok:
     If H is given input D, and while simulating D gathers enough
     information to deduce that UTM(D) would never halt, then H can
     abort its simulation and decide D never halts.
 

In other words if embedded_H was a UTM would cause Ĥ applied to ⟨Ĥ⟩ to
never halt then embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
is correctly ruled to never halt.

Exactly, IF, but H is not an UTM but a simulator *that aborts* and returns
to DD, which called it. You are reporting on what DD would hypothetically
do IF it, counter to the facts, it did NOT call the aborting simulator.
That's a different program better called something else like DD', and it
does not behave the same. You should report on the input, which DOES call
an aborting simulator. Do you get 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.