Reconstructing positive Boolean functions with shadow clustering

The problem of reconstructing the AND-OR expression of a positive Boolean function starting from a portion of its truth table is solved by adopting a proper algorithm, called shadow clustering (SC). It generates a collection of prime implicants by descending the part of the diagram of the Boolean lattice (associated with the input domain) that lies beneath the available examples. Three different versions of SC are proposed, according to the approaches adopted to perform a single move downward.