A New Constructive Approach for Creating All Linearly Separable (Threshold) Functions

A new constructive approach for creating all linearly separable functions is introduced. Balanced and unate functions on N+1 variables are created and then projected to N variables permitting to create straightforward all the linearly separable functions without needing to check for linearly separability. The method is supported by the demonstration of a theorem and numerical simulation results for small number of variables. If the results extrapolates the method may permit to test the linear separability of any function on N variables by checking monotonicity and unaleness in N+1 dimension. Furthermore, the generalization complexity of the linear threshold functions is analyzed.