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Article 5062 of comp.ai.philosophy:
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>From: daryl@oracorp.com (Daryl McCullough)
Newsgroups: comp.ai.philosophy
Subject: Functional Equivalence (Was: A rock implements every FSA)
Message-ID: <1992Apr9.214829.3723@oracorp.com>
Date: 9 Apr 92 21:48:29 GMT
Article-I.D.: oracorp.1992Apr9.214829.3723
Organization: ORA Corporation
Lines: 44

orourke@unix1.cs.umass.edu (Joseph O'Rourke) writes:

>	So here's my proposal:
>
>		Two Turing Machines are FUNCTIONALLY EQUIVALENT
>		if they make the same tape moves & writes, in the
>		same order, on every starting input tape.

>Note that there is no mention of mapping between states of the two
>machines. So in a sense, I am defining functional equivalence in
>terms of behavioral equivalence.  But it is fine-grained behavior.
>After all, if we included state transitions as part of the behavior,
>Then behaviorism = functionalism!

I think that what you have defined is behavioral equivalence, and not
functional equivalence. Behavioral equivalence is dependent on your
definition of the external interface, or what it is we are allowed to
see about the system without "opening it up". Your definition amounts
to letting people see the intermediate steps of the calculation
instead of just the final results.

To me, functional equivalence is a constraint that is imposed over and
above behavioral equivalence, and is not simply a matter of drawing
the interface at a different place.  For whatever your choice of
interface is, there is a corresponding notion of behavioral and
functional equivalence. As I said in another posting, I don't think
that functional equivalence adds anything except in the case of
nondeterministic systems, which you don't seem to be considering here.

Anyway, given your definition of equivalence for Turing Machines, I
don't understand how you extend your definition to equivalence for
other systems, such as computer programs and human brains, etc. Of
course you can write any computer program as a Turing Machine, but in
general it can be done in more than one *inequivalent* way. The usual
ways of implementing algorithms on Turing Machines don't worry too
much about what happens in intermediate calculations.

So, before I grant your definition of equivalence of Turing Machines,
I would have to know how you would extend it to other computational
systems.

Daryl McCullough
ORA Corp.
Ithaca, NY


