On Regular Message Sequence Chart Languages and Relationships to Mazurkiewicz Trace Theory

Abstract

Hierarchical Message Sequence Charts are a well-established formalism to specify telecommunication protocols. In this model, numerous undecidability results were obtained recently through algebraic approaches or relationships to Mazurkiewicz trace theory. We show how to check whether a rational language of MSCs requires only channels of finite capacity. In that case, we also provide an upper bound for the size of the channels. This enables us to prove our main result: one can decide whether the iteration of a given regular language of MSCs is regular if, and only if, the Star Problem in trace monoids (over some restricted independence alphabets) is decidable too.

Bounded MSC Communication

“…. Thus if both of them are locally strongly connected then the same holds for G. Recently it was shown in [5] that an HMSC H is ∀ b loc -bounded for some b if and only if H is locally strongly connected. The fact that H is locally strongly connected if H is ∀ b loc -bounded by some b is quite easy to see.…”

“…The fact that H is locally strongly connected if H is ∀ b loc -bounded by some b is quite easy to see. Lemma 4 below will allow us to present a simpler proof of the other direction of the result of [5], together with a sharper bound on the buffer size, which we need later. We should remark that Theorem 2.8 of [5], which corresponds to the first statement of Lemma 5, is formulated in terms of regular MSC-expressions instead of HMSCs.…”

“…Lemma 4 below will allow us to present a simpler proof of the other direction of the result of [5], together with a sharper bound on the buffer size, which we need later. We should remark that Theorem 2.8 of [5], which corresponds to the first statement of Lemma 5, is formulated in terms of regular MSC-expressions instead of HMSCs. Using the notation of [5], we can prove the following statement in the same fashion as Lemma 5.…”

“…We note that the notion of universal-local-boundedness corresponds to the notion of channel-boundedness used in [2,3,5,6] in the context of regular MSClanguages. For each of our four measures we investigate the complexity of deciding whether a given (H)MSC or nMSC satisfies a given bound on the buffer size.…”

Towards cost-aware service recovery

“…MSCs are widely adopted in describing service choreography by model exchange of messages between participants. MSCs may be interpreted as trace languages and the connection between the semantics of MSCs and traces has been established [30].Service composition modelled by high-level (or hierarchical) MSCs (hMSCs) [27], built from a collection of MSCs, may be viewed as trace synthesis. We propose use of a weighted trace language, denoted by an hMSC specification, annotating each action label with a weight (cost) and adopt semiring-based cost algebras to model parameterised costs.…”