Let X be an input space, the set of all 2n input n-tuples to a combinational circuit H with n inputs and s outputs. X has a complemented decomposition X=M+P, where P=X/M=AN+B, N is the set of integers, M is the set of noncodewords, and P is the orthogonal complement of M [1]. Piestrak considers the set of codewords where A=3 and 0≤B≤2 in designing self-testing checkers H. The code is disjoint because it applies dividers to implicants of literals. Self-testing is performed by functions of H constructed in terms of tuple literals that map codewords into codewords, which further map codewords into {0,1}. Iterative versions of the checkers in AND and OR gates could be implemented by proposed iterative methods in n.
The paper contains many mistakes, including Figure 4, a logic diagram of the STC (self-testing checker) for the 3N+2 code with five bits. The references provide the current state of the field and historical perspectives, but not necessarily prospects.
Anyone searching for mathematical models, design strategies, design heuristics, methods, or algorithms should read this good paper critically.
