  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 not
only for finite automata, but also for infinite automata, as long as they are
compact.

Formal Languages and Automata Theory;Logic in Computer Science