On Message Sequence Graphs and Finitely Generated Regular MSC Languages

Message Sequence Charts (MSCs) are an attractive visual formalism widely used to capture system requirements during the early design stages in domains such as telecommunication software. A standard method to describe multiple communication scenarios is to use message sequence graphs (MSGs). A message sequence graph allows the protocol designer to write a finite specification which combines MSCs using basic operations such as branching choice, composition and iteration. The MSC languages described by MSGs are not necessarily regular in the sense of [HM+99]. We characterize here the class of regular MSC languages that are MSG-definable in terms of a notion called finitely generated MSC languages. We show that a regular MSC language is MSG-definable if and only if it is finitely generated. In fact we show that the subclass of “bounded” MSGs defined in [AY99] exactly capture the class of finitely generated regular MSC languages.