A generalization of Shestakov's function decomposition method

Abstract

Shestakov expresses an incompletely specified Boolean function f(x/sub 1/, ..., x/sub n/) in terms of Boolean functions g/sub u/, g/sub v/ and h in the form h(g/sub u/(u/sub 1/, ..., u/sub r/), g/sub v/(v/sub 1/, ..., v/sub s/)), where {u/sub 1/, ..., u/sub r/}/spl cup/{v/sub 1/, ..., v/sub s/}={x/sub 1/, ..., x/sub 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(x/sub 1/, ..., x/sub n/) in terms of Boolean functions g and h as h(u/sub 1/, ..., u/sub r/, g(v/sub 1/, ..., v/sub 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.