Confluence of Graph Transformation Revisited

Plump, Detlef

doi:10.1007/11601548_16

Cited by 55 publications

(59 citation statements)

References 23 publications

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“…The notion of critical pairs is central in this theory, allowing for conflict detection and analysis. It was developed at first in the area of term rewriting systems (e.g., [6]) and, later, introduced in the area of graph transformation for hypergraph rewriting [7,8] and then for all kinds of transformation systems fitting into the framework of adhesive high-level replacement categories [9].…”

Section: Introductionmentioning

confidence: 99%

Conflict Detection for Graph Transformation with Negative Application Conditions

Lambers

Ehrig

Orejas

2006

Lecture Notes in Computer Science

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Abstract. This paper introduces a new theory needed for the purpose of conflict detection for graph transformation with negative application conditions (NACs). Main results are the formulation of a conflict notion for graph transformation with NACs and a conflict characterization derived from it. A critical pair definition is introduced and completeness of the set of all critical pairs is shown. This means that for each conflict, occuring in a graph transformation system with NACs, there exists a critical pair expressing the same conflict in a minimal context. Moreover a necessary and sufficient condition is presented for parallel independence of graph transformation systems with NACs. In order to facilitate the implementation of the critical pair construction for a graph transformation system with NACs a correct construction is formulated. Finally, it is discussed how to continue with the development of conflict detection and analysis techniques in the near future.

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Section: Introductionmentioning

confidence: 99%

Conflict Detection for Graph Transformation with Negative Application Conditions

Lambers

Ehrig

Orejas

2006

Lecture Notes in Computer Science

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“…Determinism directly refers to the notion of confluence (often called the Church-Rosser, or diamond, property) for Gbtls, which has also been proved as undecidable [90]. Confluence and termination are linked by Newman's lemma [82], stating that confluence coincides with local confluence if the system terminates.…”

Section: Determinism Criteriamentioning

confidence: 99%

Formal Verification Techniques for Model Transformations: A Tridimensional Classification .

Amrani¹,

Combemale²,

Levi³

et al. 2015

JOT

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In Model Driven Engineering (Mde), models are first-class citizens, and model transformation is Mde's "heart and soul". Since model transformations are executed for a family of (conforming) models, their validity becomes a crucial issue.This paper proposes to explore the question of the formal verification of model transformation properties through a tridimensional approach: the transformation involved, the properties of interest addressed, and the formal verification techniques used to establish the properties.This work is intended for a double audience. For newcomers, it provides a tutorial introduction to the field of formal verification of model transformations. For readers more familiar with formal methods and model transformations, it proposes a literature review (although not systematic) of the contributions of the field.Overall, this work allows to better understand the evolution, trends and current practice in the domain of model transformation verification. This work opens an interesting research line for building an engineering of model transformation verification guided by the notion of model transformation intent.

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“…On the other hand, the transformations However, as shown in Plump (1993) and Plump (2005), the confluence of critical pairs is not sufficient for this, and we need a slightly stronger version, called strict confluence, which adds the requirement that the preserved elements of the given steps are preserved in the merging steps. This means that elements that are not deleted by one of the original transformations steps must be preserved by the additional transformations that lead to confluence to ensure the applicability of the rules in the bigger context.…”

Section: Functional Behaviour and Efficient Executionmentioning

confidence: 99%

Formal analysis of model transformations based on triple graph grammars

Hermann

Ehrig

Golas

et al. 2014

Math. Struct. Comp. Sci.

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Triple graph grammars (TGGs) are a well-established concept for the specification and execution of bidirectional model transformations within model driven software engineering. Their main advantage is an automatic generation of operational rules for forward and backward model transformations, which simplifies specification and enhances usability as well as consistency. In this paper we present several important results for analysing model transformations based on the formal categorical foundation of TGGs within the framework of attributed graph transformation systems.Our first main result shows that the crucial properties of correctness and completeness are ensured for model transformations. In order to analyse functional behaviour, we generate a new kind of operational rule, called a forward translation rule. We apply existing results for the analysis of local confluence for attributed graph transformation systems. As additional main results, we provide sufficient criteria for the verification of functional behaviour as well as a necessary and sufficient condition for strong functional behaviour. In fact, these conditions imply polynomial complexity for the execution of the model transformation. We also analyse information and complete information preservation of model transformations, that is, whether a source model can be reconstructed (uniquely) from the target model ¶ The participation of Fernando Orejas was supported by the MEC project FORMALISM (ref. TIN2007-66923).

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Confluence of Graph Transformation Revisited

Cited by 55 publications

References 23 publications

Conflict Detection for Graph Transformation with Negative Application Conditions

Conflict Detection for Graph Transformation with Negative Application Conditions

Formal Verification Techniques for Model Transformations: A Tridimensional Classification .

Formal analysis of model transformations based on triple graph grammars

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