Re: How Partial Simulations correctly determine non-halting ---Mike Terry Error

On 5/06/24 18:49, olcott wrote:

My idea was to have the executed HH pass a portion of what is
essentially its own Turing Machine tape down to the simulated
instances of HH. It does do this now.

In other words, your idea is to have an incorrect simulation.
DD(DD) doesn't get passed a portion of any other machine's tape. If the simulation does, then the simulation is simulating something other than DD(DD). It might be simulating DD(DD,SecretParameter).

The only issue left that seems to not matter is that each simulated
HH needs to see if it must initialize its own tape.

Why shouldn't it always initialize its own tape?
  Since this

has no effect on its halt status decision I don't think it makes
any difference.
 I will double check everything to make sure there is no data passed
from the outer simulations to the inner simulations that can possibly
be used for any halt status decision by these inner simulated
instances of HH.

There are actually two different ways that it's possible to understand your program.
The inner DebugStep doesn't work the same as the outer DebugStep. Depending on which kind of viewpoint we use, we can say that the inner DebugStep is using secret information so it knows to work differently, or we can say that the inner DebugStep is normal (if directly executed), but it simulates differently from its direct execution (an incorrect simulation).

 I really appreciate your help on this.