Forme normale algébrique

En logique mathématique, la forme normale algébrique d'une fonction booléenne est une formule qui est un ou exclusif de conjonctions de variables propositionnelles ; par exemple 1 ⊕ a ⊕ b ⊕ ab ⊕ abc[1] (1 correspond à la conjonction vide). Toute fonction booléenne admet une unique forme normale algébrique de taille minimale[1].

Construction de la forme normale algébrique

Pour construire une formule normale algébrique, on part d'une forme normale disjonctive. On remplace ensuite la négation de a par (1 ⊕ a). On applique ensuite les règles de distributivité et d'absorption (a ⊕ a) = 0.


Notes et références

  1. ↑ a et b John E. Savage, Models of Computation : Exploring the Power of Computing, Addison-Wesley Longman Publishing Co., Inc., , 672 p. (ISBN 978-0-201-89539-1, lire en ligne)

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