A partial order for the M-of-N rule-extraction algorithm

We present a method to unify the rules obtained by the M-of-N rule-extraction technique, The rules extracted from a perceptron by the M-of-N algorithm are in correspondence with sets of minimal boolean vectors with respect to the classical partial order defined on vectors. Our method relies on a simple characterization of another partial order defined on Boolean vectors, We show that there exists also a correspondence between sets of minimal Boolean vectors with respect to this order and M-of-N rules equivalent to a perceptron. The gain is that fewer rules are generated with the second order, Independently, we prove that deciding whether a perceptron is symmetric with respect to two variables is NP-complete.