Anabstraction A of an fsmM consists in partitioning its states, inputs, and outputs into groups, thus turning it into a non-deterministic fsmMA. For fixed sets of states, inputs, and outputs, and abstraction generally maps a number of machinesM defined on these sets into the sameMA. We would like to find anoptimal abstractionA* which minimizes this number, while lumping the states, inputs, and outputs into a specified number of classes. We extend these ideas to an fsmM operating in a random environment, and show that the abstraction results in a probabilistic fsm \(\mathcal{M}_A \). Thinking of changes inM's output map as resulting in machinesM≠MM, we want to find anA* that minimizes the number ofMM which are such that the transition probabilities of their abstracted version Open image in new window are identical to those of the specification machine \(\mathcal{M}_A \). SuchMM arise from statistically-undetectable output faults inM. Abstractions are directly applicable to the monitoring of a complex system by an observer for deviations from correct behavior (faults). Complex systems are usually accessible through restricted interfaces, which do not allow the observer to distinguish among all states, inputs, and outputs, thus rendering some faulty transitions undetectable. An optimal interface design will minimize the number of such undetectable faults.