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Boole-De Morgan Bilattices
Yu. M. Movsisyan

It is commonly known that the free Boolean algebra on 𝑛 free generators is isomorphic to the Boolean algebra of Boolean functions of 𝑛 variables. The free bounded distributive lattice on 𝑛 free generators is isomorphic to the bounded distributive lattice of monotone Boolean functions of 𝑛 variables (R. Dedekind, 1897). In this paper we introduce the concept of Boole-De Morgan bilattice and prove a functional representation theorem for finitely generated free Boole-De Morgan bilattices. As a consequence we characterize finitely generated free distributive bilattices via functional representation. New functions alternative to Boolean functions are presented here which are applicable in cryptography and discrete mathematics, too.

Keywords: Antichain, distributive bilattice, Boole-De Morgan bilattice, free algebra, Boolean function, De Morgan function, quasi-De Morgan function, bi- De Morgan function, D-function, disjunctive (conjunctive) normal form

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