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Sur la minimisation d’une expression représentant une famille de fonctions booléennes. (French) Zbl 0588.94016

The author studies the representation of a family of Boolean functions by a unique formula \(\phi\), depending on \(p\) parameters chosen in a way that the run through of their values assures the run through the given family of functions. The proposed algorithm to construct the formula \(\phi\) permits: the minimization of the number \(p\) of parameters, the possible simplification of the calculation of the canonical form of \(\phi\) and the minimization of the normal form corresponding to the canonical one.

MSC:

94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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References:

[1] 1. M. CARVALLO, Monographie des treillis et algèbre de Boole, Gauthier Villars, Paris, 1962, 2e éd., 1966. Zbl0111.02302 · Zbl 0111.02302
[2] 2. M. CARVALLO, Principes et applications de l’analyse booléenne, Gauthier Villars, Paris, 1965, 2e éd., 1970. Zbl0213.29403 · Zbl 0213.29403
[3] 3. R. FAURE, A. KAUFMANN et M. DENIS PAPIN, Cours de calcul booléen, Albin Michel, Paris, 1963. MR170836 · Zbl 0122.25902
[4] 4. J. KUNTZMANN, Algèbre de Boole, Dunod, Paris, 1965. Zbl0123.01401 MR191755 · Zbl 0123.01401
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.