On solutions to the systems of functional Boolean equations
Sergey Seraphimovich Marchenkov, V. S. Fedorova · Journal of Applied and Industrial Mathematics · 2009
Solutions to the systems of functional Boolean equations are under study. For each of the classes P 2, T 0, T 1, S, T 01, and S 01, the problem is solved of constructing some systems of functional Boolean equations with a given set of functional constants and one functional variable whose unique solution is a given function of the class under consideration. For an arbitrary nonempty set F of n-argument Boolean functions, a system of equations with the functional constants ∨ and & is built with F as the solution set. If F is closed under transition to dual functions then the corresponding system can be constructed without functional constants.