Shadow Clustering: A Method for Monotone Boolean Function Synthesis

The problem of reconstructing the and-or expression of a monotone Boolean function starting from a fixed subset 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 portion 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. The performances of SC, in terms of optimality of the monotone Boolean function retrieved and of execution speed, have been evaluated through extensive simulations on artificial benchmarks. In addition, the possibility of using SC for general Boolean function reconstruction has been exploited, thus obtaining excellent results in comparison with classical logical synthesis techniques.