THE REAL ALGEBRAIC NORMAL FORM: FUZZY BOOLEAN LOGIC SATISFYING Δf = 0

摘要

We define real extensions f: R~n contains [0,1]~n → [0,1] (is contained in) R of Boolean functions f~B that satisfy Δf = 0 on the whole domain [0,1]~n, i.e. potential theory as first principle. We introduce the Real Algebraic Normal Form RANF ∈ Z[x_1,...,x_n] of f, a generalization of the Algebraic Normal Form ANF of f~B, and show how the RANF is related to the Disjunctive Normal Form DNF by the Reed-Muller Transform, or the Inclusion-Exclusion Principle.