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Article 1618 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: <39800@dime.cs.umass.edu>
Date: 26 Nov 91 04:09:42 GMT
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In article <centaur.691103968@cc.gatech.edu> centaur@terminus.gatech.edu (Anthony G. Francis) writes:
>
>T and M recognize the same set of languages. T and M are not equivalent
>machines because they have different space requirements. T requires the
>space for its FSA and r+j elements of tape. M requires at least r(r+j)(r+j)
>separate states. It is vastly larger, and not realizable in the same set
>of space constraints that you have placed on the Turing Machine.

Where is this "space" required? Neither of these objects are physical,
and both can be realized in a variety of ways.  You seem to believe
that a state machine must be realized as a lookup table and a Turing
machine as a lookup table and a tape. What basis is there for this
belief?  I claim that both T and M are representations of the same
mathematical object. 

>>Mathematically, both are well-defined. In what sense is it "theoretically 
>>shaky" to consider the two machines as the same?
>
>It is not theoretically shaky to consider them to represent the same language
>in the abstract. It is theoretically shaky to make statements about what
>real systems can do by noting their limitations and then ignoring those 
>limitations to prove equivalence to a theoretical class of machines that
>can't really exist. Turing Machines with finite tapes do _not_ have all
>the same properties as FSA's, and you can prove that.
>

What's the proof?

>>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. 
>
>First of all, we can't construct a FSA for the _memory_ subsystem, because
>of the physical constraints of this universe. Essentially, my point is that
>Turing Machines require unbounded amounts of storage, and for a vast collection
>of problems, actual physical storage is sufficient for an implementation of a
>Turing Machine to solve those problems. A direct implementation of a FSA for
>that same set of problems, however, is _impossible_. So, the alternatives that

Makes zero sense. An FSA is an abstract description of a finite state
discrete device or program. For example, a FSA for a single bit memory
cell might consist of two state 0 and 1, and inputs set,reset. Now
one could implement this FSA with a lisp program, a capacitor and
refresh circuit, a CMOS circuit, or even a basket and a single damn orange.
Which one of these is a "direct" implementation?

>-------------------------------Quote of the post------------------------------- 
>"Just take the money and run, and if they give you a hassle, blow them away."
>	- collected in a verbal protocol for the Bankrobber AI Project

Didn't Roger Shank say that first?



