Issue No.05 - May (1987 vol.36)

pp: 623-629

F. REremla , Research Institute for Mathematical Machines

ABSTRACT

This correspondence presents a solution of a well-known essential problem of diagnostics open till now. The method of solution is based on a straight application of mathematical structures theory 1121, [11]and on a topological representation of Boolean algebras [ 1]l[1] [ 41] The principle idea of this approach is as follows. The distribution of diagnostic information is controlled in Boolean combinational circuits (CC) by two relations generally, the first is a congruence relation and the other is a tolerance relation. This fact is given by a real construction of CC. The Boolean calculus is evidently a formal interpretation of one of these relations only. Hence, the Boolean calculus cannot be used to solve entirely such problems which are related to this distribution. If we want to disclose the essence, we have to use a more general mathematical apparatus to interpret both relations mathematically. The outline of mathematical model of CC is presented and a trace of model on its underlying set is employed to solve the problem.

INDEX TERMS

two-element Boolean algebra, Boolean combinational circuit (CC), congruence relation, essential nonfault locatability, fault equivalence class, finite Boolean construct, stuck faults, tolerance relation

CITATION

F. REremla, "General Criterion for Essential Nonfault Locatability of Logical Functions",

*IEEE Transactions on Computers*, vol.36, no. 5, pp. 623-629, May 1987, doi:10.1109/TC.1987.1676948