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From: John Smith <news2@immibis.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: How Partial Simulations correctly determine non-halting ---Mike
 Terry Error
Date: Wed, 5 Jun 2024 19:25:41 +0200
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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.
>