Lattice Functions and Equations

Lattice (Boolean) functions are algebraic functions defined over an arbitrary lattice (Boolean algebra), while lattice (Boolean) equations are equations expressed in terms of lattice (Boolean) functions. This self-contained monograph surveys recent developments of Boolean functions and equations, as well as lattice functions and equations in more general classes of lattices; a special attention is paid to consistency conditions and reproductive general solutions. The contents include: - equational compactness in semilattices and Boolean algebras; - the theory of Post functions and equations (which is very close to that of Boolean functions and equations); - a revision of Boolean fundamentals; - closure operators on Boolean functions; - the decomposition of Boolean functions; - quadratic truth equations; - Boolean differential calculus; - Boolean geometry and other topics. There is also a chapter on equations in a very general sense. Applications refer to graph theory, automata theory, synthesis of circuits, fault detection, databases, marketing and others.