Generalized transforms for multiple valued circuits and their fault detection

Simple transforms for obtaining canonical representation of multiple-valued (MV) functions in polarity k, k ∈ {0, 1,. . ., pⁿ-1}, are presented, where p and n denote the radix and the number of variables of a function. The coefficients in a canonical representation are called spectral coefficients. Various relationships between the functional values of a function and its spectral coefficients are given. Fault detection in an arbitrary MV network is considered using test patterns and spectral techniques. Upper bounds on the number of test patterns for detection of stuck-at and bridging faults at the input lines are shown to be pn and n-1, respectively. Fault detection by spectral techniques is done based on the number of spectral coefficients affected by a fault, and hence it is independent of the technology used for construction of networks and the type of fault. Test set generation for detection of any fault in {E}, where {E} denotes all faults in the network, is given. An upper bound on the number of test patterns required to detect all faults in {E} is obtained