On the construction of probabilistic diagnosers

This paper revisits the notions of observer and diagnoser, and adapts them to probabilistic automata, in a setting of weighted automata computations. In the non stochastic case, observers and diagnosers are obtained by standard elementary steps, as state augmentation, epsilon-reduction and determinization. It is shown that these steps can be adapted to probabilistic automata, and algorithms to perform them efficiently are provided. In particular, the determinization is related to a standard filtering equation that recursively computes the conditional distribution of the current state given past observations. New notions of probabilistic observers and diagnosers are provided and compared to previous constructions, and simpler derivations of the latter are proposed.