On solutions to the systems of functional Boolean equations
- 27 Downloads
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.
Key wordsfunctional Boolean equation closed class of Boolean functions
- 1.Some Selected Problems in the Theory of Boolean Functions, Ed. by A. S. Balyuk, S. F. Vinokurov, A. I. Gaydukov, et al. (Fizmatlit, Moscow, 2001) [in Russian].Google Scholar
- 5.L. Hellerstein, On Generalized Constraints and Certificates, Rutcor Research Report No. 26-98 (Rutgers Univ., Rutcor, 1998).Google Scholar
- 6.S. V. Jablonskii, G. P. Gavrilov, and V. B. Kudryavtsev, Functions of the Algebra of Logic and the Post Classes (Nauka, Moscow, 1966) [in Russian].Google Scholar
- 7.J. Kuntzman, Algébre de Boole (Dunod, Paris, 1965).Google Scholar