Re: Can returning a value change the value itself (in the Halting Problem)

From: Marc Goodman (marc.goodman_at_comcast.net)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 18:09:58 GMT

stephen@nomail.com wrote:
> In comp.theory Marc Goodman <marc.goodman@comcast.net> wrote:
> : Martin Shobe wrote:
> :> Of course the value changed. The *input* changed.
>
> : The context is a TM with access to its own state transition
> : table that can calculate the check sum of its own state
> : transition table. Do you finally see that even making
> : a "trivial" change to such a TM can cause the result produced
> : by such a TM to change? Or do we have to go through this
> : line of argument three more times?
>
> : But, both
> :> functions implement exactly the same, um, function.
>
> : You are free to call it "different input" if you want,
> : but the fact remains that if you are talking about
> : a TM with access to its own state transition table, the
> : line between "input" and "process" has been blurred.
> : To the extent that a seemingly local change to the
> : TM can have a global change to the result produced by
> : the TM.
>
> The point of a computational model is to compute mathematical functions.
> A mathematical function has an input and an output. There is no
> blurring, other than in your presentation. For your model where the program
> can inspect itself you have to decide if the program is part of the input
> or not.

Yes, it is definitely part of the input.

If the program is not part of the input, then in checksum
> example your program computes a constant function, in which case it is
> easy to write another program that computes the same function.

But it is part of the input.

If
> the program is part of the input, then it is also easy to write another
> program that computes the same function. So what mathematical function
> are you trying to compute?

A program that computes its own checksum in order to demonstrate
that making seemingly local changes to the program's code causes
a change in its results.
>
> The whole reflective code idea really does not affect the Halting
> problem at all.

I agree completely. That's not the point of this particular
argument. This argument is about whether a TM extended to have
access to its own state transition table can be trivially
"transmogrified" without changing its own results.

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