A generalization of Shestakov´s function decomposition method

Shestakov expresses an incompletely specified Boolean function f(x ₁, ..., x_n) in terms of Boolean functions g_u , g_v and h in the form h(g_u(u₁, ..., u_r), g_v(v₁, ..., v_s)), where {u₁, ..., u_r}∪{v₁, ..., v_s}={x₁, ..., x_n}. We generalize his method to multi-valued functions with partial don´t care´s represented in a compact cube-like notation; we do this using blankets, which are generalizations of set systems. Luba and Selvaraj express a Boolean function f(x₁, ..., x_n) in terms of Boolean functions g and h as h(u₁, ..., u_r, g(v₁, ..., v_s)). This method has been formalized using blankets by Brzozowski and Luba, and generalized to multi-valued functions by Brzozowski and Lou. The relations among these methods are discussed