Title: Birecurrent sets,
Abstract: A set is called recurrent if its minimal automaton is strongly connected and
birecurrent if it is recurrent as well as its reversal. We prove a series of
results concerning birecurrent sets. It is already known that any birecurrent
set is completely reducible (that is, such that the minimal representation of
its characteristic series is completely reducible). The main result of this
paper characterizes completely reducible sets as linear combinations of
birecurrent sets