Weighted diagnosis with asymmetric invalidation

Prior research has extended the classical PMC (or Symmetric Invalidation) Model to incorporate a priori weights or probabilities associated with units. We consider a similar extension to the BGM (or Asymmetric Invalidation) Model. In contrast to the PMC model, where deciding the weighted diagnosability number is co-NP complete, we show that the diagnosability number in the weighted BGM model can be obtained in O(m²) time, where m is the number of tests in the system. We also show that diagnosis in this weighted model can be performed in O(T(n)) time, where n is the number of units in the system and T(n)≈n ^2.376 is the amount of time needed to multiply two n by n matrices