Pomsets for Message Sequence Charts

Message sequence charts (MSCs) are a standardised formalism for the specification of the system’s communication behaviour that is widely used by industry. Various extensions to MSCs have recently been standardised by the ITU. This paper treats the extension of MSCs with structural operators that allow the hierarchical composition of MSCs. In particular, we propose a linear-time partial-order semantics for this extension that is based on the notion of partial-order multi-sets (pomsets, for short). We provide a compositional denotational semantics for hierarchical MSCs and show that well-known operations on pomsets correspond to the new composition operators in MSCs. The main benefit of our approach is that the semantics is conceptually rather straightforward, as opposed to the operational semantics for MSCs that is currently in the process of standardisation.