Chunks: Component Verification in CSP ∥ B

CSP||B is an approach to combining the process algebra CSP with the formal development method B, enabling the formal description of systems involving both event-oriented and state-oriented aspects of behaviour. The approach provides architectures which enable the application of CSP verification tools and B verification tools to the appropriate parts of the overall description. Previous work has considered how large descriptions can be verified using coarse grained component parts. This paper presents a generalisation of that work so that CSP vertical bar vertical bar B descriptions can be decomposed into finer grained components, chunks, which focus on demonstrating the absence of particular divergent behaviour separately. The theory underpinning chunks is applicable not only to CSP vertical bar vertical bar B specification but to CSP specifications. This makes it an attractive technique to decomposing large systems for analysing with FDR

Relational Concurrent Refinement: Timed Refinement

Data refinement in a state-based language such as Z is defined using a relational model in terms of the behaviour of abstract programs. Downward and upward simulation conditions form a sound and jointly complete methodology to verify relational data refinements, which can be checked on an event-by-event basis rather than per trace. In models of concurrency, refinement is often defined in terms of sets of observations, which can include the events a system is prepared to accept or refuse, or depend on explicit properties of states and transitions. By embedding such concurrent semantics into a relational one, eventwise verification methods for such refinement relations can be derived. In this paper we continue our program of deriving simulation conditions for process algebraic refinement by considering how notions of time should be embedded into a relational model, and thereby deriving relational notions of timed refinement

Augmenting B with Control Annotations

CSP||B is an integration of the process algebra Communicating Sequential Processes (CSP), and the B-Method, which enables consistent controllers to be written for B machines in a verifiable way. Controllers are consistent if they call operations only when they are enabled. Previous work has established a way of verifying consistency between controllers and machines by translating control flow to AMN and showing that a control loop invariant is preserved. This paper offers an alternative approach, which allows fragments of control flow expressed as annotations to be associated with machine operations. This enables designers’ understanding about local relationships between successive operations to be captured at the point the operations are written, and used later when the controller is developed. Annotations provide a bridge between controllers and machines, expressing the relevant aspects of control flow so that controllers can be verified simply by reference to the annotations without the need to consider the details of the machine operations. This paper presents the approach through two instances of annotations with their associated control languages, covering recursion, prefixing, choice, and interrupt