Verification of Statecharts Using Data Abstraction

Abstract

Abstract-We present an approach for verifying Statecharts including infinite data spaces. We devise a technique for checking that a formula of the universal fragment of CTL is satisfied by a specification written as a Statechart. The approach is based on a property-preserving abstraction technique that additionally preserves structure. It is prototypically implemented in a logicbased framework using a theorem prover and a model checker. This paper reports on the following results. (1) We present a proof infra-structure for Statecharts in the theorem prover Isabelle/HOL, which constitutes a basis for defining a mechanised data abstraction process. The formalisation is based on Hierarchical Automata (HA) which allow a structural decomposition of Statecharts into Sequential Automata. (2) Based on this theory we introduce a data abstraction technique, which can be used to abstract the data space of a HA for a given abstraction function. The technique is based on constructing over-approximations. It is structure-preserving and is designed in a compositional way. (3) For reasons of practicability, we finally present two tactics supporting the abstraction that we have implemented in Isabelle/HOL. To make proofs more efficient, these tactics use the model checker SMV checking abstract models automatically.

Investigating Airplane Safety and Security Against Insider Threats Using Logical Modeling

“…On top of the induction relation, a notion of validity of formulas in a (Kripke)-structure possibly in combination with temporal or other modalities is a possible avenue of future research. Isabelle/HOL supports such extensions, see for example [27]. Additionally we consider game theoretic extensions to the framework following the technical advances made in formalising auctions [28] and modeling [29].…”

Exploiting Hierarchy in the Abstraction-Based Verification of Statecharts Using SMT Solvers

“…The recent work of Helke and Kammüller [14] also defines abstractions over statecharts for the universal fragment of CTL model checking, which is more general than our reachability analysis. However, their main focus is on only abstracting the data and preserving the structure of the statechart, whereas in our approach abstraction on the structure is also a key feature.…”