Efficient minimization algorithms for fixed polarity AND/XOR canonical networks

Each Boolean function with fixed polarity of variables can be represented uniquely in a two-level AND/XOR form, called the generalized Reed-Muller (GRM) form. The minimization problem is to find the optimal polarity that requires the least number of product terms in the GRM representation. An efficient algorithm was developed to extract product terms of Boolean function, given a polarity of variables. It achieves the lower bound complexity. A heuristic algorithm targeting the minimization problem is proposed. It derives the polarity for every variable and extracts all product terms simultaneously. It is based on the concept of a Boolean center for minterms, which emulates the center of gravity concept in geometry. The experimental results are very encouraging