Foundations for Behavioural Model Elaboration Using Modal Transition Systems

Abstract

Modal Transition Systems (MTS) are an extension of Labelled Transition Systems (LTS) that have been shown to be useful to reason about system behaviour in the context of partial information. MTSs distinguish between required, proscribed and unknown behaviour and come equipped with a notion of refinement that supports incremental modelling where unknown behaviour is iteratively elaborated into required or proscribed behaviour. A particularly useful notion in the context of software and requirements engineering is that of “merge”. Merging two consistent models is a process that should result in a minimal common refinement of both models where consistency is defined as the existence of one common refinement. One of the current limitations of MTS merging is that a complete and correct algorithm for merging has not been developed. Hence, an engineer attempting to merge partial descriptions may be prevented to do so by overconstrained algorithms or algorithms that introduce behaviour that does not follow from the partial descriptions being merged. In this thesis we study the problems of consistency and merge for the existing MTSs semantics - strong and weak semantics - and provide a complete characterization of MTS consistency as well as a complete and correct algorithm for MTS merging using these semantics. Strong and weak semantics require MTS models to have the same communicating alphabet, the latter allowing the use of a distinguished unobservable action. In this work we show that the requirement of fixing the alphabet for MTS semantics and the treatment of observable actions are limiting if MTSs are to support incremental elaboration of partial behaviour models. We present a novel observational semantics for MTS, branching alphabet semantics, inspired by branching LTS equivalence, which supports the elaboration of model behaviour including the extension of the alphabet of the system to describe behaviour aspects that previously had not been taken into account. Furthermore, we show that some unintuitive refinements allowed by weak semantics are avoided, and prove a number of theorems that relate branching refinement with alphabet refinement and consistency. These theorems, which do not hold for other semantics, support the argument for considering branching alphabet as a sound semantics to support behaviour model elaboration