Non-simplifying Graph Rewriting Termination

So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly with trees. In a former paper, we showed the benefit of encoding linguistic structures by graphs and of using graph rewriting rules to compute on those structures. Justified by some linguistic considerations, graph rewriting is characterized by two features: first, there is no node creation along computations and second, there are non-local edge modifications. Under these hypotheses, we show that uniform termination is undecidable and that non-uniform termination is decidable. We describe two termination techniques based on weights and we give complexity bound on the derivation length for these rewriting system.Comment: In Proceedings TERMGRAPH 2013, arXiv:1302.599

Preliminary Version

Abstract Visual rewriting techniques are increasingly used to model transformations of systems specified through diagrammatic sentences. Graph transformations, in particular, are a widespread formalism with several applications, from parsing to model animation or transformation. Although a wealth of rewriting models have been proposed, differing in the expressivity of the types of rules and in the complexity of the rewriting mechanism, basic results concerning the formal properties of these models are still missing for many of them. In this paper, we propose a contribution towards solving the termination problem for rewriting systems with external control mechanisms for rule application. In particular, we obtain results of more general validity by extending the concept of transformation unit to high-level replacement systems, a generalization of graph transformation systems. For the resulting highlevel replacement units, we state and prove several abstract properties based on termination criteria. Then, we instantiate the high-level replacement systems by attributed graph transformation systems and present concrete termination criteria. These are used to show the termination of some replacement units needed to express model transformations as a consequence of software refactoring

Proving Termination of Graph Transformation Systems using Weighted Type Graphs over Semirings

We introduce techniques for proving uniform termination of graph transformation systems, based on matrix interpretations for string rewriting. We generalize this technique by adapting it to graph rewriting instead of string rewriting and by generalizing to ordered semirings. In this way we obtain a framework which includes the tropical and arctic type graphs introduced in a previous paper and a new variant of arithmetic type graphs. These type graphs can be used to assign weights to graphs and to show that these weights decrease in every rewriting step in order to prove termination. We present an example involving counters and discuss the implementation in the tool Grez

Asserting the Correctness of Software Language Translations

While building a new language, we assign its semantics by mapping its syntax onto a semantic domain. To do so, we can either (i) do it operationally, by means of small-step morphisms within the same semantic-domain; or (ii) by means of a translation (syntax-to-syntax transformation), onto a target language that has already an operational semantics defined. Despite the fact that it is possible to build the set of syntactic correspondences from a given translation, it is still not clear how we can assert about the correctness of these syntactic correspondences in w.r.t. both the source and target language's underlying semantics.In this paper, we combine the above described techniques by analyzing the translation and establishing a semantic relation between the respective operational semantics, in order to assert the correctness of that translation. We demonstrate our approach with a concrete translation between two languages: State Machines and Petri Nets; and decide about its correctness by using their respective operational semantics as oracles. Finally, we discuss about the validity of our assertions in w.r.t. language translations in general

Verification of Model Transformations to Refactoring Mobile Social Networks

Verification of model processing programs, where only the definitions of the program and the languages of the models to be transformed are analyzed, has become a fundamental issue in model-based software engineering. This analysis may become very complex, but it is performed only once and the results are independent from concrete input models. The formal background of verification methods for graph rewriting-based model transformations has become a subject of research recently. In previous work, we have provided fundamental formal and algorithmic background of a (semi-)automated verification approach for graph transformations. This work concludes these components and put them together to introduce the implementation of a verification system fully integrated into a model transformation framework, VMTS. The strong points of our approach is its usability, its implementation in an existing tool, and its extendibility, which are demonstrated on a case study in the application domain of mobile centric social networks. Our results show that the verification of graph rewriting-based model transformations can be largely automated

A Termination Criterion for Graph Transformations with Negative Application Conditions

Termination of graph transformations is in general undecidable, but it is possible to prove it for specific systems by checking for sufficient conditions. In the presence of rules with negative application conditions, the difficulties increase. In this paper we propose a different approach to the identification of a (sufficient) criterion for termination, based on the construction of a labelled transition system whose states represent overlaps between the negative application condition and the right hand side that can give rise to cycles

Termination Criteria for Model Transformation

Nowadays the usage of model transformations in software engineering has become widespread. Considering current trends in software development such as model driven development (MDD), there is an emerging need to develop model manipulations such as model evolution and optimisation, semantics definition, etc. If a model transformation is described in a precise way, it can be analysed lateron. Models, especially visual models, can be described best by graphs, due to their multi-dimensional extension. Graphs can be manipulated by graph transformation in a rule-based manner. Thus, we specify model transformation by graph transformation. This approach offers visual and formal techniques in such a way that model transformations can be subjects to analysis. Various results on graph transformation can be used to prove important properties of model transformations such as its functional behaviour, a basic property for computations. Moreover, certain kinds of syntactical and semantical consistency properties can be shown on this formal basis

Automated Verification by Declarative Description of Graph Rewriting-Based Model Transformations

Usually, verification of graph rewriting-based model transformations is performed manually, however, the industrial applications require automated methods. In several cases, transformation developers are interested in the offline analysis, when only the definition of the transformation and the specification of the modeling languages are taken into account. Hence, the analysis must be performed only once, and the results are independent from the concrete input models. For this purpose, transformations should be specified in a formalism that can be automatically analyzed. Based on our previous work that presented the mathematical background, this paper provides a platform-independent, declarative formalism for the specification of graph rewriting-based model transformations, and demonstrates its applicability on a case study of refactoring mobile-based social network models. Our results prove that several functional properties of the model transformations can be automatically verified, moreover, the capabilities of our methods can be extended in the future

Rewriting Systems for Reachability in Vector Addition Systems with Pairs

15 pagesInternational audienceWe adapt hypergraph rewriting system to a generalization of Vector Addition Systems with States (VASS) that we call vector addition systems with pairs (VASP). We give rewriting systems and strategies, that allow us to obtain reachability equivalence results between some classes of VASP and VASS. Reachability for the later is well known be equivalent to reachability in Petri nets. VASP generalize also Branching Extension of VASS (BVASS) for which it is unknown if they are more expressive than VASS. We consider here a more restricted notion of reachability for VASP than that for BVASS. However the reachability decision problem corresponding is already equivalent to decidability of the provability in Multiplicative and Exponential Linear Logic (MELL), a question left open for more than 20 years