Developing Topology Discovery in Event-B

We present a formal development in Event-B of a distributed topology discovery algorithm. Distributed topology discovery is at the core of several routing algorithms and is the problem of each node in a network discovering and maintaining information on the network topology. One of the key challenges is specifying the problem itself. Our specification includes both safety properties, formalizing invariants that should hold in all system states, and liveness properties that characterize when the system reaches stable states. We establish these by appropriately combining proofs of invariant preservation, event refinement, event convergence, and deadlock freedom. The combination of these features is novel and should be useful for formalizing and developing other kinds of semi-reactive systems, which are systems that react to, but do not modify, their environment

On the realization of reactive systems

A new notion of realization of reactive systems is defined. Realization is defined as a relation between the states of two transition systems, the specification and the implementation, in which events are classified as input, output or internal. This new definition attempts to model the correct interaction between a system and its environment. The differences with other definitions of refinement and realization are discussed.Postprint (published version

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Refinement Calculus of Reactive Systems

Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on monotonic predicate transformers, which transform sets of post-states into sets of pre-states. To model reactive systems, we introduce monotonic property transformers, which transform sets of output traces into sets of input traces. We show how to model in this semantics refinement, sequential composition, demonic choice, and other semantic operations on reactive systems. We use primarily higher order logic to express our results, but we also show how property transformers can be defined using other formalisms more amenable to automation, such as linear temporal logic (suitable for specifications) and symbolic transition systems (suitable for implementations). Finally, we show how this framework generalizes previous work on relational interfaces so as to be able to express systems with infinite behaviors and liveness properties

Action Contraction

The question we consider in this paper is: “When can a combination of fine-grain execution steps be contracted into an atomic action execution”? Our answer is basically: “When no observer can see the difference.” This is worked out in detail by defining a notion of coupled split/atomic simulation refinement between systems which differ in the atomicity of their actions, and proving that this collapses to Parrow and Sjödin’s coupled similarity when the systems are composed with an observer

Towards Symbolic Model-Based Mutation Testing: Combining Reachability and Refinement Checking

Model-based mutation testing uses altered test models to derive test cases that are able to reveal whether a modelled fault has been implemented. This requires conformance checking between the original and the mutated model. This paper presents an approach for symbolic conformance checking of action systems, which are well-suited to specify reactive systems. We also consider nondeterminism in our models. Hence, we do not check for equivalence, but for refinement. We encode the transition relation as well as the conformance relation as a constraint satisfaction problem and use a constraint solver in our reachability and refinement checking algorithms. Explicit conformance checking techniques often face state space explosion. First experimental evaluations show that our approach has potential to outperform explicit conformance checkers.Comment: In Proceedings MBT 2012, arXiv:1202.582