Z-diagnosis was proposed for speeding up diagnostic fault simulation by identifying in an efficient manner fault pairs that are guaranteed to be distinguished by a fault detection test set. Z-diagnosis is based on z-sets, which capture information about the outputs to which fault effects may be propagated. We introduce a dual concept of a-diagnosis that is based on a-sets, which capture fault activation conditions. More generally, a-sets include necessary assignments for the detection of target faults. We use a -sets to speed up diagnostic fault simulation in two ways, as part of a test set independent process and as part of a test set dependent process. The test set dependent process uses only logic simulation of the test set to identify fault pairs that are guaranteed to be distinguished by the test set. We present experimental results to demonstrate the speed up in diagnostic fault simulation obtained by using a -sets in addition to z-sets.