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Summary: Compositional Refinement for Hierarchical Hybrid
Systems ?
Rajeev Alur 1 , Radu Grosu 2 , Insup Lee 1 , and Oleg Sokolsky 1
1 Department of Computer and Information Science, University of Pennsylvania
2 Department of Computer Science, State University of New York at Stony Brook
Abstract. In this paper, we develop a theory of modular design and refine
ment of hierarchical hybrid systems. In particular, we present compositional
tracebased semantics for the language Charon that allows modular specifi
cation of interacting hybrid systems. For hierarchical description of the system
architecture, Charon supports building complex agents via the operations of
instantiation, hiding, and parallel composition. For hierarchical description
of the behavior of atomic components, Charon supports building complex
modes via the operations of instantiation, scoping, and encapsulation. We de
velop an observational trace semantics for agents as well as for modes, and
define a notion of refinement for both, based on trace inclusion. We show this
semantics to be compositional with respect to the constructs in the language.
1 Introduction
Modern software design paradigms promote hierarchy as one of the key constructs
for structuring complex specifications. We are concerned with two distinct notions
of hierarchy. In architectural hierarchy , a system with a collection of communicating
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