On the Inadmissible Class of Multiple-Valued Faulty-Functions under Stuck-at Faults

There exists a class of Boolean functions, called root-functions, which can never appear as faulty response in irredundant two-level-AND-OR combinational circuits even when any arbitrary multiple stuck-at faults are injected. However, for multi-valued logic circuits, root-functions are not yet well understood. In this work, we characterize some of the multiple-valued root-functions in the context of irredundant two-level AND-OR multiple-valued circuit realizations. As in the case of binary logic, such a function can never appear as a faulty-function in the presence of any stuck-at fault. We present here a preliminary study on multiple-valued root-functions for ternary (3-valued) logic circuits, and identify a class of n-variable ternary root-functions using a recursive method called concatenation. Such an approach provides a generalized mechanism for identifying a class of root-functions for other p-valued(p > 3), n-variable, two-level AND-OR logic circuits. Furthermore, we establish an important connection between root-functions and the classical latin-square functions.