## A Static Analysis Technique for Graph Transformation Systems (2001)

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Venue: | In Proc. of CONCUR ’01 |

Citations: | 43 - 17 self |

### BibTeX

@INPROCEEDINGS{Baldan01astatic,

author = {Paolo Baldan and Andrea Corradini and Barbara König},

title = {A Static Analysis Technique for Graph Transformation Systems},

booktitle = {In Proc. of CONCUR ’01},

year = {2001},

pages = {381--395},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we introduce a static analysis technique for graph transformation systems. We present an algorithm which, given a graph transformation system and a start graph, produces a nite structure consisting of a hypergraph decorated with transitions (Petri graph) which can be seen as an approximation of the Winskel style unfolding of the graph transformation system. The fact that any reachable graph has an homomorphic image in the Petri graph and the additional causal information provided by transitions allow us to prove several interesting properties of the original system. As an application of the proposed technique we show how it can be used to verify the absence of deadlocks in an innite-state Dining Philosophers system.

### Citations

1298 |
Symbolic Model Checking
- McMillan
- 1993
(Show Context)
Citation Context ...invariants [16] to model checking based onsnite ? Research partially supported by the EC TMR Network GETGRATS, by the ESPRIT Working Group APPLIGRAPH, and by the MURST project TOSCA. complete prexes [=-=13]-=-, 1 the rich literature on GTSs does not contain many contributions to the static analysis of such systems (see [11, 12]). In this paper we present an original analysis technique for a class of (hyper... |

579 |
Nets: An Introduction
- Reisig, Petri
- 1985
(Show Context)
Citation Context ...of the specication, for example by allowing the early detection of logical errors. While several static analysis techniques have been proposed for Petri nets, ranging from the calculus of invariants [=-=16-=-] to model checking based onsnite ? Research partially supported by the EC TMR Network GETGRATS, by the ESPRIT Working Group APPLIGRAPH, and by the MURST project TOSCA. complete prexes [13], 1 the ric... |

327 |
Handbook of Graph Grammars and Computing by Graph Transformation
- Rozenberg, ed
(Show Context)
Citation Context ...ce of deadlocks in an innite-state Dining Philosophers system. 1 Introduction Graphs are very useful to describe complex structures in a direct and intuitive way. Graph Transformation Systems (GTSs) [=-=18-=-] add to the static description given by graphs a further dimension which models graph evolution via the application of rules, usually having local eects only. GTSs have been recognized to have fruitf... |

178 | W.: An improvement of McMillan’s unfolding algorithm
- Esparza, Römer, et al.
- 2002
(Show Context)
Citation Context ...in such a way that the resultingsnite structure, thesnite complete prex, contains as much information as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([=-=8, 9, 19-=-]). The unfolding construction has been generalized to graph transformation systems [17, 2, 1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfoldi... |

174 |
Introduction to the algebraic theory of graph grammars (A survey
- Ehrig
- 1979
(Show Context)
Citation Context ...n VR VL ) and the edges of R. Observe that the (images of) the nodes in L are \preserved", i.e., not aected by the rewriting step. The reader which is familiar with the double-pushout (DPO) appro=-=ach [-=-4] to graph rewriting would have recognized that our rules (L; R; ) can be seen as DPO rules (Ls- VL ,! R) and that our notion of rewriting is equivalent to a DPO construction. Hence compared to gene... |

162 |
Petri Nets are Monoids
- Meseguer, Montanari
- 1990
(Show Context)
Citation Context ... L have the same label, (iii) the morphism 'L is surjective on nodes, (iv) VL and VR 'R (V K ) do not contain isolated nodes. 2.2 Petri nets In this subsection wesx some basic notation for Petri nets =-=[16,-=- 14]. Given a set A we will denote by A the free commutative monoid over A, whose elements will be called multisets over A. Given a function f : A ! B, by f : A ! B we denote its monoidal extensio... |

144 |
Branching Processes of Petri Nets
- Engelfriet
- 1991
(Show Context)
Citation Context ...his condition, in the case of branching processes, allows one to interpret each transition as an occurrence ofsring of a transition in the original net, uniquely determined by its causal history (see =-=[7]-=-). Similarly, here it aims at avoiding the presence of multiple events which are indistinguishable for what regards the behaviour of the system. Hereafter all the considered Petri nets will be implici... |

114 |
Model Checking Using Net Unfoldings
- Esparza
- 1993
(Show Context)
Citation Context ...in such a way that the resultingsnite structure, thesnite complete prex, contains as much information as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([=-=8, 9, 19-=-]). The unfolding construction has been generalized to graph transformation systems [17, 2, 1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfoldi... |

42 | Decidable approximations of sets of descendants and sets of normal forms
- Genet
- 1998
(Show Context)
Citation Context ...-hand side again, if we have already done the same unfolding step in its past, since this might lead to innitely many steps. There are some similarities, to be further investigated, with the work in [=-=10]-=- where the sets of descendants and of normal forms of term rewriting systems are approximated by constructing an approximation automaton. The coverability of a marking can be decided by computing the ... |

34 | Unfolding and event structure semantics for graph grammars
- Baldan, Corradini, et al.
- 1999
(Show Context)
Citation Context ...formation as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([8, 9, 19]). The unfolding construction has been generalized to graph transformation systems =-=[17, 2, -=-1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfolding, but the analogy with thesnite prex construction of nets ends here. In fact the GTSs we c... |

33 | Modelling concurrent computations: from contextual Petri nets to graph grammars
- Baldan
- 2000
(Show Context)
Citation Context ...formation as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([8, 9, 19]). The unfolding construction has been generalized to graph transformation systems =-=[17, 2, -=-1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfolding, but the analogy with thesnite prex construction of nets ends here. In fact the GTSs we c... |

31 | Unfolding and Finite Prefix for Nets with Read Arcs
- Vogler, Semenov, et al.
- 1998
(Show Context)
Citation Context ...a way that the resulting finite structure, the finite complete prefix, contains as much information as the unfolding itself, and can therefore be used for checking efficiently behavioural properties (=-=[8, 9, 19]-=-). The unfolding construction has been generalized to graph transformation systems [17, 2, 1], and the technique we propose makes use of unfolding steps for generating the (finite) approximated unfold... |

27 |
Parallel Composition and Unfolding Semantics of Graph Grammars
- Ribeiro
- 1996
(Show Context)
Citation Context ...formation as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([8, 9, 19]). The unfolding construction has been generalized to graph transformation systems =-=[17, 2, -=-1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfolding, but the analogy with thesnite prex construction of nets ends here. In fact the GTSs we c... |

21 |
Concurrent Graph and Term Graph Rewriting
- Corradini
- 1996
(Show Context)
Citation Context ...ormalism for concurrent systems, GTSs are known to be more expressive than (Place/Transition) Petri nets, which can be seen, indeed, as GTSs acting on discrete graphs only (i.e., multisets of tokens) =-=[3-=-]. However, even if the theory of GTSs is nowadays well developed and a number of tools for the support of specications based on this formalism have been developed, GTSs are not yet used as widely as ... |

13 |
Integration of Graph Transformation and Temporal Logic for the Specification of Distributed Systems
- Koch
- 2000
(Show Context)
Citation Context ...e ESPRIT Working Group APPLIGRAPH, and by the MURST project TOSCA. complete prexes [13], 1 the rich literature on GTSs does not contain many contributions to the static analysis of such systems (see [=-=11, 12]-=-). In this paper we present an original analysis technique for a class of (hyper) graph transformation systems, which, given a system and a start hypergraph, extracts from them an approximated unfoldi... |

10 | A general framework for types in graph rewriting
- König
- 2005
(Show Context)
Citation Context ...e ESPRIT Working Group APPLIGRAPH, and by the MURST project TOSCA. complete prexes [13], 1 the rich literature on GTSs does not contain many contributions to the static analysis of such systems (see [=-=11, 12]-=-). In this paper we present an original analysis technique for a class of (hyper) graph transformation systems, which, given a system and a start hypergraph, extracts from them an approximated unfoldi... |

7 |
Unfolding and pre for nets with read arcs
- Vogler, Semenov, et al.
(Show Context)
Citation Context ...in such a way that the resultingsnite structure, thesnite complete prex, contains as much information as the unfolding itself, and can therefore be used for checking eciently behavioural properties ([=-=8, 9, 19-=-]). The unfolding construction has been generalized to graph transformation systems [17, 2, 1], and the technique we propose makes use of unfolding steps for generating the (nite) approximated unfoldi... |