From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!mips!swrinde!gatech!cc.gatech.edu!terminus!centaur Tue Mar 24 09:56:52 EST 1992
Article 4559 of comp.ai.philosophy:
Xref: newshub.ccs.yorku.ca comp.ai.philosophy:4559 sci.philosophy.tech:2337
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!mips!swrinde!gatech!cc.gatech.edu!terminus!centaur
>From: centaur@terminus.gatech.edu (Anthony G. Francis)
Newsgroups: comp.ai.philosophy,sci.philosophy.tech
Subject: Re: A rock implements every FSA
Message-ID: <centaur.700937150@cc.gatech.edu>
Date: 18 Mar 92 16:45:50 GMT
References: <1992Mar17.224156.9177@bronze.ucs.indiana.edu>   <1992Mar17.231452.9979@husc3.harvard.edu> <1992Mar18.045939.3084@bronze.ucs.indiana.edu> <1992Mar18.095140.9984@husc3.harvard.edu>
Sender: news@cc.gatech.edu
Organization: Georgia Tech College of Computing
Lines: 38

zeleny@zariski.harvard.edu (Mikhail Zeleny) writes:
>DC:
>>Of course C and D will be found in the table.  That's my point.  They
>>won't be found in the rock, though.  Putnam's construction doesn't
>>even *define* any physical states corresponding to C and D, let alone
>>ensure that the right transition relation holds between them.
>>Therefore the claim that the system in question implements the FSA is
>>groundless.  At best, it implements a "trace" of a particular run
>>of the FSA, as Joseph O'Rourke nicely put it.
MZ:
>This is easy: first, you interpret the states of Putnam's automaton as
>ordered pairs <state, input> of a FSA (cf. the relevant comments on p.124);
>follow this by running through enough input/state combinations to exhaust
>the finite combinatorial possibilities afforded by the machine's table.
>Finally, you do the mapping.  In this way, there will be no counterfactual
>possibilities left unaccounted for.

Impossible. As a quick check to any basic automata text will show you,
a FSA can support input strings of unbounded (e.g., in layman's terms, 
infinite) size. The pumping lemma (that nasty little theorem that proves
that no FSA can accept strings longer than its number of states without
accepting all similiar strings containing some common repeating substring)
won't buy your way out of this one; the set of strings is still infinite
in size and therefore the number of ordered pairs in the above example
is infinite as well and cannot be mapped to any real rock.

If you're willing to devise another mapping, go ahead; however, any
such mapping of Putnam's type would, of course, be _post hoc_ and 
valueless in any scientific setting, regardless of its theoretical validity.
-Anthony Francis
--
Anthony G. Francis, Jr.  - Georgia Tech {Atl.,GA 30332}
Internet Mail Address: 	 - centaur@cc.gatech.edu
UUCP Address:		 - ...!{allegra,amd,hplabs,ut-ngp}!gatech!prism!gt4864b
-------------------------------Quote of the post------------------------------ 
"Cerebus doesn't love you ... Cerebus just wants all your money" 
		- Cerebus the Aardvark, from a _Church and State_ T-shirt
------------------------------------------------------------------------------


