A Kleene theorem and model checking algorithms for existentially bounded communicating automata

The behavior of a network of communicating automata is called existentially bounded if communication events can be scheduled in such a way that the number of messages in transit is always bounded by a value that depends only on the machine, not the run itself. We show a Kleene theorem for existentially bounded communicating automata, namely the equivalence between communicating automata, globally cooperative compositional message sequence graphs, and monadic second order logic. Our characterization extends results for universally bounded models, where for each and every possible scheduling of communication events, the number of messages in transit is uniformly bounded. As a consequence, we give solutions in spirit of Madhusudan (2001) for various model checking problems on networks of communicating automata that satisfy our optimistic restriction.