Directional derivatives of multi-valued logical functions

In this paper, we consider directional derivatives of multi-valued logical functions. First, we give a definition of directional derivatives for multi-valued logical functions. Second, we present a new algebraical method and establish a new algorithm to compute directional derivatives for multi-valued logical functions by using the semi-tensor product. Finally, the obtained results are applied to the fault detection of multi-valued digital circuits, and a complete test set of stuck-at faults is obtained.