## Causal Message Sequence Charts (2007)

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Citations: | 8 - 2 self |

### BibTeX

@MISC{Gazagnaire07causalmessage,

author = {Thomas Gazagnaire and Shaofa Yang and Loïc Hélouët and Blaise Genest and P. S. Thiagarajan},

title = { Causal Message Sequence Charts},

year = {2007}

}

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### Abstract

... Charts, UML's sequence diagrams) have been widely studied in the last decade. Scenario languages embed the expressive power of Mazurkiewicz traces, and consequently, several problems such as model checking are undecidable for these languages. Despite their expressive power, most of scenario languages can only model finitely generated behaviors that can be described as the concatenation of patterns from a finite set. However, non-finitely generated behaviors such as sliding windows frequently occur in asynchronous distributed systems. Several extensions of Message Sequence Charts have been proposed to capture non-finitely generated behaviors, but these variants embed the expressive power of automata communicating via unbounded channels (and thus of Turing Machines), making their analysis even more intractable. We propose a new extension of Message Sequence Charts that can model non-finitely generated MSC languages without embedding the expressive power of communicating automata, and study its properties.

### Citations

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Citation Context ...t, its second component Future(D) is constant, hence Future(D) =Future(C). Since C ⊆ D, we have that q!p(m ′ ) is a label of an event of D and is not in Future(C) =Future(D). Using Tarjan’s algorithm =-=[16]-=-, we can compute in quadratic time the partition of A (e,f) into maximal strongly connected components (for each set X ⊆ 2 Σ , we partition the subpart of A (e,f) with a constant second component bein... |

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Citation Context ...s the visual extensions Vis(M) = {M1, M2} of causal MSC M. We next need to define a composition operation for causal MSCs. To this end, for each process p in P, we fix a concurrent alphabet (Σp, Ip) (=-=[4]-=-), where Ip is an 4 A Q A Qsindependence relation over the alphabet of actions Σp, i.e. Ip ⊆ Σp×Σp is a symmetric and irreflexive relation. We denote the dependence relation (Σp ×Σp)−Ip by Dp. For con... |

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Citation Context ....fr 4 School of Computing, NUS, Singapore thiagu@comp.nus.edu.sg Abstract. Scenario languages based on Message Sequence Charts (MSCs) and related notations have been widely studied in the last decade =-=[14, 13, 2, 9, 6, 12, 8]-=-. The high expressive power of scenarios renders many basic problems concerning these languages undecidable. The most expressive class for which several problems are known to be decidable is one which... |

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Citation Context ...tive operation. Note that in case B and B ′ are MSCs and Dp = Σp × Σp for every p, then the result of B ⊚ B ′ is the asynchronous concatenation (also called weak sequential composition) of B with B ′ =-=[15]-=-, which we denote by B ◦ B ′ . We also remark that the concatenation of causal MSCs is different from the concatenation of traces. The concatenation of trace [u]p with [v]p is the trace [uv]p. However... |

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Citation Context ...finitely generated. It follows that (regular/globally-cooperative) causal HMSCs are strictly more powerful than (regular/globally-cooperative) HMSCs. Another extension of HMSCs is Compositional HMSCs =-=[7]-=-, or CHMSCs for short. CHMSCs generalize HMSCs by allow dangling message-sending and message-reception events, i.e. where the message pairing relation ≪ is only a partial non-surjective mapping contai... |

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Citation Context ....fr 4 School of Computing, NUS, Singapore thiagu@comp.nus.edu.sg Abstract. Scenario languages based on Message Sequence Charts (MSCs) and related notations have been widely studied in the last decade =-=[14, 13, 2, 9, 6, 12, 8]-=-. The high expressive power of scenarios renders many basic problems concerning these languages undecidable. The most expressive class for which several problems are known to be decidable is one which... |

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Citation Context ...ults in a higher complexity [5]. It is also worth noting that without the restriction to safety (realizability), compositional HMSC languages embed the full expressive power of communicating automata =-=[3]-=- and consequently inherit all their undecidability results. This paper proposes another approach to extend HMSCs in a tractable manner. The key feature is to allow the events belonging to a lifeline t... |

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Citation Context ....fr 4 School of Computing, NUS, Singapore thiagu@comp.nus.edu.sg Abstract. Scenario languages based on Message Sequence Charts (MSCs) and related notations have been widely studied in the last decade =-=[14, 13, 2, 9, 6, 12, 8]-=-. The high expressive power of scenarios renders many basic problems concerning these languages undecidable. The most expressive class for which several problems are known to be decidable is one which... |

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Citation Context ...tate� automaton AH over Σ that recognizes Lin(H). Furthermore, AH has at most |N| 2 · 2 |Σ| · 2 |N|·|Σ|·2m� |N|·|Σ|·2 m states, where m = max{|B| |B ∈B}with |B| denoting the number of events in B. In =-=[11]-=-, the regularity of linearization languages of regular HMSC was proved by using an encoding into connected traces and building a finite state automaton which recognizes such connected traces. In our c... |

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Citation Context ...s. p Ip Iq m = { (p!q(m), p!r(o)), (p!r(o), p!q(m)) } = { } = { } I r q n r p o r p q r Fig. 7. A globally-cooperative causal HMSC that is not existentially bounded We shall adapt the notion of atoms =-=[1, 9]-=- and the techniques from [6]. Let us first introduce a notion of decomposition of causal MSCs into basic parts. Definition 4. A causal MSC B is a basic part (w.r.t. the trace alphabets {(Σp,Ip)}) if t... |

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1 |
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Citation Context ...ffective verification. This is so since for a suitable choice of K, the set of K-bounded linearizations of any globally cooperative HMSC is regular, and this suffices for doing effective verification =-=[6]-=-. Unfortunately, this result uses Kuske’s encoding [11] into traces that is based on the existence of an (existential) bound on communication. Consider the causal HMSC H of Figure 5. It is globally co... |

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