help with boolean algebra

From: Jim Newton (jimka_at_rdrop.com)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 12:20:07 +0100

Hi everyone, I'm writing a LISP program to solve a certain
types of systems of boolean equastions. Does anyone
know a lot about boolean algebra? It would be nice to
talk to someone about my ideas. The algorithms are not
specific to lisp but the implementation is.

What I need are some identities envolving several
boolean variables with the operations of XOR and AND.

Notation: !A represents (not a)
and AB represents (and a b)
and !AB represents (and (not a) b)
and + represents XOR -- A + B <=> (xor a b)

I have the following three identies and have generalized them
to several variables.

t = A + !A
t = A + !AB + !A!B
t = AB + !AB + A!B + !A!B

Are there other identies envolving XOR and AND and NOT?
All others that i can think of are derivable from these
three.

For example: AB => A ( => implies)
is equivalent to : t = !(AB) + A + A!(AB)
which apparently simplifies to: t = A + !AB + !A!B

I'll be very happy to share the lisp code with anyone interested.

-jim

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