Finite Equations in n Unknowns
Fonctions booléennes très incomplètes. Représentation par des sommes de monômes
Formulas of the general solutions of Boolean equations.
Four-part semigroups - semigroups of Boolean operations
Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
Function classes and relational constraints stable under compositions with clones
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.