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Article 1577 of comp.ai.philosophy:
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>From: yodaiken@chelm.cs.umass.edu (victor yodaiken)
Newsgroups: comp.ai.philosophy
Subject: Re: Daniel Dennett
Message-ID: <39729@dime.cs.umass.edu>
Date: 25 Nov 91 13:19:08 GMT
References: <1991Nov23.214707.1663@cc.gatech.edu> <39701@dime.cs.umass.edu> <centaur.691029638@cc.gatech.edu>
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In article <centaur.691029638@cc.gatech.edu> centaur@terminus.gatech.edu (Anthony G. Francis) writes:
>yodaiken@chelm.cs.umass.edu (victor yodaiken) writes:
>
>
>On the other hand, claiming that a realizable TM can be reduced to an 
>unrealizable FSA is not only theoretically shaky, it also dodges
>the question of what real-world systems actually use. Of course a theory of
>notation and denotaion can't be implemented on a FSA. But a subset of that
>theory - that might apply to finite human beings - might be implemented
>on a Turing Machine.

Still confused, I resort to an example. 
Consider the following two abstract machines. T is a turing machine
that, when started on a tape containing an input of k or fewer symbols from
a r element alphabet will compute some function, never using more than
r+j squares of tape. M is a FSA with state set  of all the triples of the
form (inputing,p,q)  and (working,s,p,q)  where p ranges over all integers
between 1 and r+j and q ranges over all r+j tuples over the alphabet and
a blank character. We interpret p as the position of the head, and q as the
contents of the tape. The initial state of M is (inputing,1,blank-tuple)
  The input alphabet for M consists of inputs "start"
(input,a) for each a over the input alphabet of T, and "step". 
The transition function for M is such that if it gets an input
(input, b) in a state (inputing,p,(t_1,....,t_{r+j}) ) it will go
to state (inputing,p,(t_1,...,t_{p-1},b,t{p+1},...t_{r+j})). If
it gets an input start in a state (inputing,p,q) it will go to 
(working,1,q), and if gets an input "step" in state
(working,p,q) it will do what T would do in the same configuration.

In what sense if M less realizable than T?  Mathematically, both are
well-defined. In what sense is it "theoretically shaky" to consider
the two machines as the same?
Physically, the number of states depends on our parameters,
so one could not guess how to build them, or even if it were possible
(e.g., set r = Ackermann(10000000,100000000) and give up). It appears to me
that we have two distinct representations of the same object.

As for your example of a Sun computer, constructing a FSA representation is
probably less hard than constructing a pure TM representatation. At least
for the FSA we have a theory of automata products which will allow us
to construct a FSA for memory, one for disk .... and combine them. TM
products are quite a bit messier --- because of the tape. 


