New approach to derivative calculation of multi-valued logical functions with application to fault detection of digital circuits

This study investigates the directional derivative of multi-valued logical functions with application to fault detection of multi-valued digital circuits. Firstly, the authors study the calculation problem of directional derivatives of multi-valued logical functions by using the semi-tensor product. Several new results and a new algorithm are obtained to calculate the directional derivative. Then, the achieved results are applied to the fault detection of multi-valued digital circuits. A complete test set of stuck-at faults is obtained. Finally, two illustrative examples are presented to demonstrate the effectiveness of the authors´ method.