Communicating Hierarchical State Machines

Rajeev Alur, Sampath Kannan, and Mihalis Yannakakis

Hierarchical state machines are finite state machines whose states themselves can be other machines. In spite of their popularity in many modeling tools for software design, very little is known concerning their complexity and expressiveness. In this paper, we study these questions for hierarchical state machines as well as for communicating hierarchical state machines, that is, finite state machines extended with both hierarchy and concurrency. We present a comprehensive set of results characterizing (1) the complexity of the reachability, emptiness and universality problems, (2) the complexity of the language inclusion and equivalence problems, and (3) the succinctness relationships between different types of machines.

Automata, Languages, and Programming: Proceedings of the 26th International Conference, (ICALP'99), Lecture Notes in Computer Science 1644, Springer, pp. 169--178, 1999.