Dear Martin,
Many thanks for these explanations...
They point exactly what I was looking for.
a very last question : Is there a link between
ring structure GF(2)[a,b,c] / (a^2-a, b^2-b, c^2-c) where + == xor and *
== and
and Boolean predicates over variables a, b, c with operators "or == |"
and "and == &".
I know I can code "a or b" by 1 - (1-a)*(1-b) == a*b + a + b
in order to translate an boolean expression to an algebraic one.
But can I return from a*b+a+b to "a or b" ?
I'm looking if it's possible to get normal and-expand form from any
expression, and or-expand form.
By example, these normal forms are
not(a xor b) == (a and b) or (not a and not b) # for the or-expand form.
a xor b == (a and not b) or (not a and b)
not(a xor b) == (a or b) and (not a or not b) # for the and-expand form.
a xor b == (a or not b) and (not a or b)
Many thanks.
F. in France.
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