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Article 4907 of comp.ai.philosophy:
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>From: orourke@unix1.cs.umass.edu (Joseph O'Rourke)
Newsgroups: comp.ai.philosophy
Subject: Re: A rock implements every FSA
Message-ID: <46023@dime.cs.umass.edu>
Date: 3 Apr 92 17:41:21 GMT
References: <1992Apr2.164457.24191@oracorp.com>
Sender: news@dime.cs.umass.edu
Reply-To: orourke@ sophia.smith.edu (Joseph O'Rourke)
Organization: Smith College, Northampton, MA, US
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I think the following two statements of daryl@oracorp.com (Daryl McCullough)
cancel one another out, so to speak:

In article <1992Apr2.164457.24191@oracorp.com>:
 >We haven't come to a consensus about what it means for two state
 >machines to be equivalent, except that I have proposed that they are
 >equivalent if there is a mapping between corresponding states that
 >preserves the transition relation.

In article <1992Apr2.155348.19580@oracorp.com>:
 >The single-state machine can be made functionally equivalent
 >to the 5-colour-map-checker by adding a clock (so that no two consecutive
 >states are the same).

To me the functional equivalence of the map-checker and the single-
state machine shows that your definition of functional equivalence
is flawed.
	Perhaps the definition would more accord with intuition
if the state-mappings were between Turing Machines with tapes?
For a realistic map-checker program, if written as a TM, would repeatedly 
return to some of its states, with only the contents of memory different
(e.g., by incrementing various loop counters and so on), whereas
the single-state-cross-time would never return to old states.
The definition of functional equivalence would also need to demand a
mapping between tapes.
	I don't have a precise definition to propose (surely this must
have been studied by TM researchers?), but with reasonable
assumptions, it seems that it would be possible to prove that
the single-state machine + clock is not functionally equivalent
to any 5-color-map-checker.


