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Abstract. Hierarchical Automata represent a structured model of statecharts. They are formalized in Isabelle/HOL. The formalization is on two levels. The first level is the set-based semantics; the second level exploits the tree-like structure of the hierarchical automata to represent them using Isabelle's datatypes and primitive recursive functions. Thereby the proofs about hierarchical automata are simplified. In order to ensure soundness of this twofold approach we define a mapping from the latter to the former representation and prove that it preserves the defining properties of hierarchical automata.

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Abstract. Hierarchical automata (HAs) represent a structured model of statecharts previously formalized in Isabelle/HOL. The present work extends this framework by an abstraction technique for HAs defined on infinite data spaces. This structure preserving abstraction enables the connection of the framework to the model checker SMV. This paper reports on the following results (a) We discuss abstractions of sequential automata, from which HAs are composed. Here we focus on the special problems of synchronous models and examine the feasibility of constructions for over-and underapproximations in order to preserve CTL properties. (b) Based on this results we describe a compositional abstraction technique, which can be applied to HAs. (c) We extend the formalization of HAs in Isabelle/HOL by suitable operators to construct abstractions inside the logic. (d) We present an efficient implementation of the abstraction process outside of the logic, which is integrated in the formalization by the oracle interface of Isabelle.