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In this paper, we present a method and a tool to build symbolic labelled transition systems from B specifications. The tool, called GeneSyst, can take into account refinement levels and can visualize the decomposition of abstract states in concrete hierarchical states. The resulting symbolic transition system represents all the behaviors of the initial B event system. So, it can be used to reason about them. We illustrate the use of GeneSyst to check security properties on a model of electronic purse.

We present a fixpoint semantics of event systems. The semantics is presented in a general framework without concerns of fairness. Soundness and completeness of rules for deriving "leads-to" properties are proved in this general framework. The general framework is instantiated to minimal progress and weak fairness assumptions and similar results are obtained. We show the power of these results by deriving sufficient conditions for "leads-to" under minimal progress proving soundness of proof obligations without reasoning over state-traces.

In this report, we present a formal model of fair iteration of events for B event systems. The model is used to justify proof obligations for basic liveness properties and preservation under refinement of general liveness properties. The model of fair iteration of events uses the dovetail operator, an operator proposed by Broy and Nelson to model fair choice. The proofs are mainly founded in fixpoint calculations of fair iteration of events and weakest precondition calculus.