CSP theorems for communicating B machines

Abstract

Recent work on combining CSP and B has provided ways of describing systems comprised of components described in both B (to express requirements on state) and CSP (to express interactive and controller behaviour). This approach is driven by the desire to exploit existing tool support for both CSP and B, and by the need for compositional proof techniques. This paper is concerned with the theory underpinning the approach, and proves a number of results for the development and verification of systems described using a combination of CSP and B. In particular, new results are obtained for the use of the hiding operator, which is essential for abstraction. The paper provides theorems which enable results obtained (possibly with tools) on the CSP part of the description to be lifted to the combination. Also, a better understanding of the interaction between CSP controllers and B machines in terms of non-discriminating and open behaviour on channels is introduced, and applied to the deadlock-freedom theorem. The results are illustrated with a toy lift controller running example

Java implementation platform for the integrated state‐ and event‐based specification in PROB

“…An abstract B+CSP specification cannot currently be refined and decomposed into a distributed system. In [29], an approach for composing combined B and CSP specifications-CSP B-is presented. Work is in progress on practically applying a similar composition technique for B+CSP.…”

Relational concurrent refinement part II: Internal operations and outputs

“…The angelic has, however, been advocated in the context of integrating formal methods. For example, Treharne and Schneider argue in [41] that the angelic model is more natural when CSP controllers are combined with B components in integrations of CSP and B. In particular, the CSP acts as a non-discriminating controller which cannot block on the values that the B component provides.…”

Comparing Formal Verification Approaches of Interlocking Systems

“…These lead to two further safety properties, namely: -"no train on a route with a green signal" -this encodes the check that the route path of the clear table covers all detection sections between two marker boards; and -"no deviation from the designated route" -this encodes the check that all points on a route path are in the right position to guide the train from the start marker board to the end marker board of a route. Specification Language for the system model is CSP||B [22], a combination of the process algebra CSP and the B specification language that allows for a combination of event-based and state-based modelling. We use event-based modelling to capture state changes, e.g., a train moves from one track to the other is represented as move.A.B; we use state-based modelling to represent the rules that guide the behaviour of the interlocking, e.g., the conditions under which a route can be set or cancelled.…”