Lattice Structures For Bisimilar Probabilistic Automata

The paper shows that there is a deep structure on certain sets of bisimilar Probabilistic Automata (PA). The key prerequisite for these structures is a notion of compactness of PA. It is shown that compact bisimilar PA form lattices. These results are then used in order to establish normal forms (in the sense of [4]) not only for finite automata, but also for infinite automata, as long as they are compact.