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Article 4781 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
Summary: one state -> infinite # of states?
Message-ID: <45656@dime.cs.umass.edu>
Date: 28 Mar 92 20:38:09 GMT
References: <1992Mar27.145107.12415@oracorp.com>
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Reply-To: orourke@sophia.smith.edu (Joseph O'Rourke)
Organization: Smith College, Northampton, MA, US
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[Pardon me if this appears twice...]:
In article <1992Mar27.145107.12415@oracorp.com> 
	daryl@oracorp.com (Daryl McCullough) writes:

 >Now, with this notion of implementation, the Zeleny machine, together
 >with a couple of lookup tables, can implement *any* FSM. The Zeleny
 >machine has states defined by a pair of integers <n,y> and has the
 >transition relation: <n,y> --> <n,y+1>.
 >
 >Okay, so the mapping: M(<n,0>) = State_n
 >                      M(<n, y+1>) = T(M(<n,y>))

Was the "Zeleny machine" suggested in a posting, or are you refering
to a private discussion?
	Suppose you have a simple machine that only makes transitions
on input, such as the one I used as an example in an earlier posting
(<45426@dime.cs.umass.edu>):

        FSA state   Input   ==>   FSA state
	---------   -----         ---------
	    A         0               A
            A         1               B
	    B         0               B
            B         1               A

Should we then say that T, your transition-on-no-input function,
is the identity function, so that T(A) = A and T(B) = B?  That 
seems to make the most sense.  If so, then your mapping between 
machines becomes

	M( <A,0>   ) = A
	M( <A,y+1> ) = T( M( <A,y> ) ) = A

Therefore, if I understand the proposal, this simple two-state
machine includes among its corresponding Z-machine states <A,0>, <A,1>,
<A,2>, ..., all of which are mapped to A by M.  Or to reverse
the mapping, the single state A is modeled by an infinite number
of states in the Z-machine.
	Is this right?


