Geodesic
Essential Arity Gap of Boolean Functions
Serdica Journal of Computing, Tome 2 (2008) no. 3, pp. 249-266.

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In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions with a given arity gap. The Full Conjunctive Normal Forms are also sum of conjunctions, in which all variables occur.
Keywords: Essential Variable, Identification Minor, Essential Arity Gap 
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Shtrakov, Slavcho. Essential Arity Gap of Boolean Functions. Serdica Journal of Computing, Tome 2 (2008) no. 3, pp. 249-266. http://geodesic.mathdoc.fr/item/SJC_2008_2_3_a2/