## Reasoning about Sequential and Branching Behaviours of Message Sequence Graphs (0)

Venue: | In ICALP ’00, LNCS 2076 |

Citations: | 23 - 3 self |

### BibTeX

@INPROCEEDINGS{Madhusudan_reasoningabout,

author = {P. Madhusudan},

title = {Reasoning about Sequential and Branching Behaviours of Message Sequence Graphs},

booktitle = {In ICALP ’00, LNCS 2076},

year = {},

pages = {396--407},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study the model-checking problem of message-sequence graphs (MSGs). In the sequential setting, we consider the set of message-sequence charts (MSCs) represented by an MSG and tackle specifications given in monadic second-order logic. We show that this problem, without any restrictions on the MSGs, is decidable. We then turn to branching behaviours of MSGs, define a notion of an unfolding of an MSG, and show that the model-checking problem on unfoldings is also decidable. Our results are stronger and imply that, over an appropriate universe, satisfiability and synthesis of MSCs and MSGs, respectively, are decidable.

### Citations

361 |
On a decision method in restricted second order arithmetic
- Büchi
- 1960
(Show Context)
Citation Context ... . Then Lemma 1 smoothly extends to MSO formulas over innite MSCs generated by thesnite collection ofsnite atomic MSCs in the MSG. All we need to do is to work over nondeterministic Buchi automata [4,=-= 17, -=-18] and use the property that the languages these automata accept are eectively closed under union, complement and projection. The analogous model-checking and satisability theorems for innite MSCs wi... |

198 | An Analyzer for Message Sequence Charts
- Alur, Holzmann, et al.
- 1996
(Show Context)
Citation Context ...ntial machines. Since MSCs and MSGs have a formal semantics, they are amenable to analysis. The issue of model-checking MSCs and MSCs dened by an MSG has been an area of active study in recent years [=-=1, 11, 14, 13, 2, 9-=-]. Automated verication of MSGs could enable engineers to check whether the design requirements have been met and whether it describes the set of desirable (or undesirable) behaviours correctly. Alur ... |

141 | Model checking of message sequence charts
- Alur, Yannakakis
- 1999
(Show Context)
Citation Context ...ntial machines. Since MSCs and MSGs have a formal semantics, they are amenable to analysis. The issue of model-checking MSCs and MSCs dened by an MSG has been an area of active study in recent years [=-=1, 11, 14, 13, 2, 9-=-]. Automated verication of MSGs could enable engineers to check whether the design requirements have been met and whether it describes the set of desirable (or undesirable) behaviours correctly. Alur ... |

101 | On transition graphs having a decidable monadic theory - Caucal - 1996 |

85 |
Automata on in objects
- Thomas
- 1990
(Show Context)
Citation Context ...re of Thomas' adaptation of the proof by Buchi [3] and Elgot [6] that classes of languages dened by monadic second-order formulas oversnite strings correspond to the class of regular languages (see [1=-=7, 18]-=-). This proof works by inductively associating with every formula '(X 1 ; : : : ; X k ) an automaton A' over words that encode interpretations of the variables over the structure and accept the word i... |

82 | Tutorial on Message Sequence Charts
- Rudolph, Graubmann, et al.
- 1996
(Show Context)
Citation Context ...s of MSCs and MSGs, respectively, are decidable. 1 Introduction Message sequence charts (MSC) are a popular visual formalism used to describe design requirements of concurrent message-passing systems =-=[16, 10]-=-. They are used to describe behaviours of systems in early models of system design. An MSC describes a single partially-ordered execution of the system and a collection of these diagrams formalize the... |

54 | Deciding properties for message sequence charts
- Muscholl, Peled, et al.
- 1998
(Show Context)
Citation Context ...ntial machines. Since MSCs and MSGs have a formal semantics, they are amenable to analysis. The issue of model-checking MSCs and MSCs dened by an MSG has been an area of active study in recent years [=-=1, 11, 14, 13, 2, 9-=-]. Automated verication of MSGs could enable engineers to check whether the design requirements have been met and whether it describes the set of desirable (or undesirable) behaviours correctly. Alur ... |

45 | An expressively complete linear time temporal logic for Mazurkiewicz traces
- Thiagarajan, Walukiewicz
- 1997
(Show Context)
Citation Context ...s are perhaps more amenable to reasoning about MSCs than logics which specify properties of the linearizations of an MSC. Logics such as monadic second-order logic, or an adaptation of the logic LTrL =-=[19-=-], or localised logics such as mLTL [15] can all be seen as structural logics which when dened over MSCs appropriately will be decidable. Turning to the theoretical interest of our results, the study ... |

36 |
automata, and logic, in Handbook of Formal Languages
- Thomas, Languages
- 1997
(Show Context)
Citation Context ...satises ' if ' is true in G and we denote this by G j= '. In the proofs, we work with a dierent set of formulas that is as expressive, but which has no formulas withsrst-order variables (as done in [1=-=8-=-]). This restricted syntax has atomic formulas X Y , Singleton(X) and X l !Y . Other formulas are '_ , :' and 9X'(X). It is easy to see that this syntax is exactly as expressive as the original one. ... |

32 | A theory of regular MSC languages
- Henriksen, Mukund, et al.
(Show Context)
Citation Context ...tically identiable sub-class of MSGs called bounded MSGs, for which they prove that the linearizations form a regular set of sequences, and thereby solve the modelchecking problem for this class. In [=-=7, 9-=-], the authors dene a notion of regular MSC-languages which are recognizable by distributed communicatingsnite-state devices and study their properties. The global device is forced to besnite-state by... |

23 | Regular Collections of Message Sequence Charts
- Henriksen, Mukund, et al.
- 2000
(Show Context)
Citation Context |

21 |
Weak second-order arithmetic and automata
- Buchi
- 1960
(Show Context)
Citation Context ...decidable is to show that for any property ', the strings x 2 such that mscM;h (x) j= ' form a regular subset of . The proof follows the structure of Thomas' adaptation of the proof by Buchi [3] and Elgot [6] that classes of languages dened by monadic second-order formulas oversnite strings correspond to the class of regular languages (see [17, 18]). This proof works by inductively associat... |

21 | Monadic second order logic on tree-like structures - Walukiewicz |

8 |
Verification of message sequence charts via template matching
- Levin, Peled
- 1997
(Show Context)
Citation Context |

6 |
On message sequence graphs and generated regular MSC languages
- Henriksen, Mukund, et al.
- 2000
(Show Context)
Citation Context ...global device is forced to besnite-state by constraining channels to have a bounded capacity. However, this class of languages are not contained in, nor contain, the class of languages dened by MSGs [=-=-=-8]. It is also shown that bounded MSGs dene only regular MSC-languages and hence it follows from their results that one can decide specications written in MSO on such bounded MSGs. In this paper, the ... |

3 |
Reasoning about message passing in state environments
- Meenakshi, Ramanujam
- 2000
(Show Context)
Citation Context ...g about MSCs than logics which specify properties of the linearizations of an MSC. Logics such as monadic second-order logic, or an adaptation of the logic LTrL [19], or localised logics such as mLTL =-=[1-=-5] can all be seen as structural logics which when dened over MSCs appropriately will be decidable. Turning to the theoretical interest of our results, the study of innite graphs which have a decidabl... |

2 |
Decision problems of automata and related arithmetics
- Elgot
- 1961
(Show Context)
Citation Context ...o show that for any property ', the strings x 2 such that mscM;h (x) j= ' form a regular subset of . The proof follows the structure of Thomas' adaptation of the proof by Buchi [3] and Elgot [6] that classes of languages dened by monadic second-order formulas oversnite strings correspond to the class of regular languages (see [17, 18]). This proof works by inductively associating with every... |

1 |
Reasoning about Sequential and Branching properties of Message Sequence Graphs
- Madhusudan
- 2001
(Show Context)
Citation Context ...Gs in Section 3. In Section 4 we dene the notion of an unfolding of an MSG and show how we can reason about it. Due to space restrictions we provide only the main ideas| more details can be found in [=-=12]-=-. 2 Preliminaries A message sequence chart (MSC) is a diagram which depicts a single partiallyordered execution of a distributed message-passing system. For example, consider the MSC depicted on the l... |

1 |
Message sequence charts and decision problems on Mazurkiewicz traces
- Muscholl, Peled
- 1999
(Show Context)
Citation Context |