Fault Detection in Network Realizations of Systems of Monotone Boolean Functions

The minimal disjunctive normal form of a monotone Boolean function does not contain variables with negation and, therefore, permits a network realization without inverters, which is attractive in itself. On the other hand, a set of conjunctions without negations does not possess properties of a separating system, which creates an obstacle to fault detection in a network. Nevertheless, in this paper, we prove that, under some conditions, a network remains testable, and a considerable reduction of the volume of computations while constructing diagnosis facilities is achieved.