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Summary: Communicating Hierarchical State Machines
Rajeev Alur
University of Pennsylvania
alur @ cis.upenn.edu
Sampath Kannan
University of Pennsylvania
kannan @ cis.upenn.edu
Mihalis Yannakakis
Columbia University
mihalis@cs.columbia.edu
August 17, 2005
Abstract
Hierarchical state machines are nite 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, nite state machines extended with both hierarchy and concurrency. We present a com-
prehensive 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 di erent types of machines.
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