Towards a Theory of Regular MSC Languages

Abstract

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. It is fruitful to have mechanisms for specifying and reasoning about collections of MSCs so that errors can be detected even at the requirements level. We propose, accordingly, a notion of regularity for collections of MSCs and explore its basic properties. In particular, we provide an automata-theoretic characterization of regular MSC languages in terms of finite-state distributed automata called bounded message-passing automata. These automata consist of a set of sequential processes that communicate with each other by sending and receiving messages over bounded FIFO channels. We also provide a logical characterization in terms of a natural monadic second-order logic interpreted over MSCs.A commonly used technique to generate a collection of MSCs is to use a Message Sequence Graph (MSG). We show that the class of languages arising from the so-called locally synchronized MSGs constitute a proper subclass of the languages which are regular in our sense. In fact, we characterize the locally synchronized MSG languages as the subclass of regular MSC languages that are finitely generated.

Synthesis and Control of Asynchronous and Distributed Systems

“…Each MSG defines thus an MSC language L(MSG). It is undecidable whether the language L(MSG) is regular [66], but this language is always existentially bounded (the bound B may be computed from G).…”

“…An MSC language L is existentially bounded if, for some B, at least one linear extension of every MSC in the set may be executed using channels with capacity B [65]. Regular and regular bounded MSC languages coincide [66] (the bound B may be computed from a regular expression of L). A useful notation for sets of MSCs is Message Sequence Graphs (MSGs).…”

“…The similar problem for proper implementations (in which every run may be extended to a successful run) can be decided in EXPSPACE. More permissive implementations are studied in [66] and [60]. The problem is to construct, for a regular MSC language L, a CFM with set of messages M × X such that L = ηL(CFM), where η is the abstraction map defined with η(p(e)) = p(e), η(p!q(m, x)) = p!q(m), and η(p?q(m, x)) = p?q(m).…”

“…Such implementations may always be obtained by pairing messages m with finite informations on the p-view of the sending process, coded with time stamps defined and used like in [50]. Implementations are non-deterministic in [66], deterministic in [60], but they are not proper.…”

Non-local Choice and Beyond: Intricacies of MSC Choice Nodes

“…MSCs), in this paper we use the mathematically more convenient notion of a message sequence graph (MSG). Since these concepts are equally expressive (see [8]) this is a valid and common strategy. An MSG is a finite directed graph in which each node is labeled with a bMSC (basic MSC), and there is one initial and one terminal node.…”