The computer: a definition.

From: William R. Buckley <wrb_at_wrbuckley.com>
Date: Wed Nov 19 22:50:14 2003

> On Wed, 19 Nov 2003, William R. Buckley wrote:
>
> > >From Daniel I. A. Cohen's book, Introduction To Compuer Theory,
> > pp 788
> >
> > >>Definition. If a Turning Machine (TM) has the property that for every
> > word
> > >>it accepts, at the time it halts, it leaves one solid string
> of a's and
> > b's on
> > >>its Tape starting in cell i, we call it a computer. The
> input string we
> > call
> > >>the input (or, string of input numbers), and we identify it
> as a sequence
> > >>of nonnegative integers. The string left on the Tape we call
> the output
> > >>and identify it also as a sequence of nonnegative integers.
> >
> > The discussion continues,
> >
> > "Now we finally know what a computer is. Those expensive boxes of
> > electronics sold as computers are only approximations to the real McCoy.
> > For one thing, they almost never come with an infinite memory
> like a true
> > TM."
>
> William, you are completely contradicting yourself at this point. You
> started out asserting that all computers are Turning machines, then you
> quoted the source above which is saying that they really aren't, and
> implying exactly what Tony Duell said a few messages ago, which is that
> they aren't because they don't have infinite memory.
>

I did not contradict myself. I admit fully that the ideal TM has infinite
memory.
I also note that typical, contemporary computers are not exactly a TM. Yet,
they are computationally equivalent, and if you do not understand that
point,
then you do not understand the foundations of computer science.

Also, you must like the verbage, as you seem compelled to comment.

William R. Buckley
Received on Wed Nov 19 2003 - 22:50:14 GMT