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From: flake@scr.siemens.com (Gary William Flake)
Subject: Re: turing machine...who cares?
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Date: Tue, 30 Apr 1996 15:04:41 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai:38561 comp.ai.philosophy:40938 comp.ai.alife:5508

In article <4m55bj$5gi@nntp.seflin.lib.fl.us>,
Ralph Silverman <z007400b@bcfreenet.seflin.lib.fl.us> wrote:
>
>	turing's machine
>	is an abstraction of computer systems
>	that predates the computer systems
>	we have...

True.

>	and actually,
>		resembles them little!

True on a superficial level.  False if you consider that they compute
the same functions.

>	why embrace this antiquated and
>		peculiar
>	abstraction now?

For the same reason that biologists study fruit flies.  If you want to
make a profound statement about computers, it should apply to all
computers, not just one particular model.  You could base all of your
analysis on a Cray, but the fact that Turing machines (along with
lambda calculus, general recursive functions, and lisp) are simple
makes it easier to prove general statements that apply to all
computers.

>	for example...
>	normally,
>		actual computers
>	are routinely expected to support
>		generalized arithmetic division operations.
>	there is reason to believe that no
>	algorithym for this on turing's machine
>	has been published and proven valid!!!
>	a period of time

This is patently false.  For example, it is not too difficult to prove
that a random access machine and a Turing machine are equal in
computing power.  Take your favorite division algorithm that runs on a
random access machine, and use the emulation algorithm from the proof
as a subroutine.  Voila.

Better yet, use a simplified version of lisp and represent integers as
unary lists, and rationals by two integers.  For fun you can write a
square root operation.  It may take a year to finish, but it is
amazing that it can be done with little more than the cons, cdr, and
car operators.

>		>50 years
>	has passed since turing's paper published...
>	is it not getting a little late?
>	and
>	is there any responsible opinion that
>		turing's machine
>	is a effective basis for the study of
>		algorithyms
>	now
>	???	

Listen.  No one is suggesting that a Turing machine be built.  As an
applied device a TM would be very cumbersome.  But as a theoretical
device it is tremendously useful.  Why?  Primarily because it is so
simple.  But more importantly, a TM as a model of computation is
universal.  Pick your favorite program that runs on your home PC.  If
it runs in time f(n), where n is the input length, then there exists a
TM that runs th same program in time g(f(n)), where g() is a
polynomial (and, therefore, well-behaved).  This means that the two
models of computation are for the most part "equivalent" in processing
speed as well.

I hope this clarifies things for you.

>Ralph Silverman
>z007400b@bcfreenet.seflin.lib.fl.us

-- 
Gary W. Flake, Ph.D., flake@scr.siemens.com, Vox:609-734-3676, Fax:609-734-6565
Project Manager and MTS,  Adaptive Information and Signal Processing Department
Siemens Corporate Research,  755 College Road East,  Princeton, NJ  08540,  USA
