Re: Extending binary NOR

From: Bob Badour <bbadour_at_pei.sympatico.ca>
Date: Fri, 22 Sep 2006 14:18:28 GMT
Message-ID: <UgSQg.33802$9u.304822_at_ursa-nb00s0.nbnet.nb.ca>


David Cressey wrote:

> This is an offshoot of the discussion of Idempotence and "Replication
> Sensitivity". I prefer to start a new discussion, because the thread drift
> is too great.
>
> Extending the concept of binary NOR so that is can operate on a column of
> values, rather than only two values, seems to me to be a useful
> generalization.
>
> Marshall has called attention to the difference between his generalization
> which relies on folding, and Pamela's which does not. I have a problem
> with the result you get by folding NOR, in terms of the usefulness of such a
> generalized operation.
> logical NOR is commutative, but not associative. e.g.
>
> (T nor T) nor F) is not equal to (T nor (T nor F))
>
> Thus the result of applying folded NOR to a column of values is dependent on
> the order of the values in the column, if the column has more than 2 values.
> This looks ugly to me, as I prefer to think of a column of values as
> representing a set.
>
> I prefer the generalization made by the manufacturers of standard NOR gates.
> There are standard NOR gates with 3 or 4 inputs, and I believe their output
> is independent of the "order" of the inputs. I believe they yield false in
> any of the inputs are true, and yield true otherwise. I think this
> generalization models what Marshall has called n-ary NOR.
>
> I think this generalization is more useful, if you are going to use
> generalized gates to model boolean logic. I also think that this
> generalization is more useful if you are going to build a computer out of
> gates. And I think either one of these assertions follows from the other.
> Notice I'm saying "more useful" not "more correct".
>
>
> I want to provide some reference for this discussion, although I'm not
> suggesting that these references are necessarily definitive. If you start
> in the Wikipedia Article entitled "Zeroth order logic" and click on
> "Logical NOR" and then click on "NOR gate", you get a description of the
> NOR gate that generalizes to 4 inputs. Incidentally, I couldn't get to
> this article by a direct search in Wikipedia, but I may be doing something
> wrong in my use of Wikipedia.
>
> Also, in passing, all three of the above articles are useful references for
> moving this discussion forward.

As Marshall already pointed out, n-ary NOR is the negation of a folded binary OR. Since binary OR is commutative, associative and idempotent, the n-ary NOR is just an expression based on an aggregate function.

In other words, n-ary NOR is based on binary OR and not on binary NOR. Received on Fri Sep 22 2006 - 16:18:28 CEST

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