Architectures logicielles et matérielles : Cours, études de by Jean-Charles Fernandez, Visit Amazon's Fabienne Lagnier

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La taille effective du ROBDD d´epend de l’ordre choisi pour les variables. Un probl`eme est de trouver un ordre optimal. D’autres m´ethodes de simplification de BDD consistent `a ajouter des informations suppl´ementaires sur les arcs, on parle alors de BDD typ´es. Le lecteur pourra trouver des informations d´etaill´ees sur ces m´ethodes dans [Bry86]. 38 Alg`ebre de Boole et fonctions bool´eennes a b c b c (a) a a b 1 f f f 0 b c b c 1 c 1 0 0 (b) Fig. 10 – a) La mise en commun des feuilles `a 1 et `a 0.

2 Obtention d’une forme polynˆ omiale De nombreuses technologies de r´ealisation des circuits n´ecessitent une forme polynˆomiale. Le crit`ere d’optimisation est alors le nombre de monˆomes apparaissant dans la forme polynˆomiale puis le nombre de variables dans ces monˆomes. Un certain nombre de techniques de simplification respectant ce crit`ere ont ´et´e mises au point et int´egr´ees dans les outils modernes de CAO. Nous montrons ici comment obtenir une forme polynˆomiale r´eduite `a partir d’un tableau de Karnaugh.

3 Formes de Lagrange En appliquant successivement le th´eor`eme de Shannon sur toutes les variables de la fonction, on obtient une forme polynˆomiale compos´ee de tous les monˆomes canoniques affect´es de coefficients correspondant aux valeurs de la fonction. f (1, 1) Cette forme est appel´ee premi`ere forme de Lagrange. Toute fonction poss`ede une et une seule forme de ce type. C’est une expression canonique. On simplifie en g´en´eral cette forme en supprimant tous les monˆomes dont le coefficient est 0 et en enlevant les coefficients `a 1.

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