Development of Correct Graph Transformation Systems

Pennemann, Karl-Heinz

doi:10.1007/978-3-540-87405-8_48

Cited by 43 publications

(82 citation statements)

References 43 publications

(118 reference statements)

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“…It is not necessarily complete: spurious counterexamples can occur, because the theorem above only describes a sufficient condition. Addressing this approach-inherent drawback requires a more complex notion of pattern implication, which is, in general, an undecidable problem [13]. However, previous [5] and current evaluation show the applicability of our approach even without such extensions.…”

Section: Step 3: Analysis Of Sequencesmentioning

confidence: 88%

“…More general approaches discussing implication of (unrestricted) graph constraints can be found in [10,13].…”

Section: Formal Modelmentioning

confidence: 99%

“…[2]). In contrast to that, the SeekSat/ProCon tool [10,13] is able to prove correctness of graph programs with respect to pre-and postconditions specified as nested graph constraints; however, it may require too expensive (cf. [5]) or infeasible computations.…”

Section: Introductionmentioning

confidence: 99%

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k-Inductive Invariant Checking for Graph Transformation Systems

Dyck

Giese

2017

Lecture Notes in Computer Science

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While offering significant expressive power, graph transformation systems often come with rather limited capabilities for automated analysis, particularly if systems with many possible initial graphs and large or infinite state spaces are concerned. One approach that tries to overcome these limitations is inductive invariant checking. However, the verification of inductive invariants often requires extensive knowledge about the system in question and faces the approach-inherent challenges of locality and lack of context.To address that, this report discusses k-inductive invariant checking for graph transformation systems as a generalization of inductive invariants. The additional context acquired by taking multiple (k) steps into account is the key difference to inductive invariant checking and is often enough to establish the desired invariants without requiring the iterative development of additional properties.To analyze possibly infinite systems in a finite fashion, we introduce a symbolic encoding for transformation traces using a restricted form of nested application conditions. As its central contribution, this report then presents a formal approach and algorithm to verify graph constraints as k-inductive invariants. We prove the approach's correctness and demonstrate its applicability by means of several examples evaluated with a prototypical implementation of our algorithm.

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Section: Step 3: Analysis Of Sequencesmentioning

confidence: 88%

“…More general approaches discussing implication of (unrestricted) graph constraints can be found in [10,13].…”

Section: Formal Modelmentioning

confidence: 99%

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k-Inductive Invariant Checking for Graph Transformation Systems

Dyck

Giese

2017

Lecture Notes in Computer Science

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“…Definition 1 (partial monomorphism ( [15], adjusted)). A partial monomorphism p ∶ A ⨽ ⇀ B is a 2-tuple p = ⟨a, b⟩ of monomorphisms a, b with dom(a) = dom(b), dom(p) = codom(a), and codom(p) = codom(b).…”

Section: Foundationsmentioning

confidence: 99%

“…[4]). On the other hand the SeekSat/ProCon tool [15,11] is able to prove correctness of graph programs with respect to pre-and postconditions specified as nested graph constraints without such limitations, but requires potentially expensive computations.…”

Section: Introductionmentioning

confidence: 99%

Inductive Invariant Checking with Partial Negative Application Conditions

Dyck

Giese

2015

Lecture Notes in Computer Science

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Bibliografische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.dnb.de/ abrufbar. Graph transformation systems are a powerful formal model to capture model transformations or systems with infinite state space, among others. However, this expressive power comes at the cost of rather limited automated analysis capabilities. The general case of unbounded many initial graphs or infinite state spaces is only supported by approaches with rather limited scalability or expressiveness. In this paper we improve an existing approach for the automated verification of inductive invariants for graph transformation systems. By employing partial negative application conditions to represent and check many alternative conditions in a more compact manner, we can check examples with rules and constraints of substantially higher complexity. We also substantially extend the expressive power by supporting more complex negative application conditions and provide higher accuracy by employing advanced implication checks. The improvements are evaluated and compared with another applicable tool by considering three case studies. Universitätsverlag 5

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Formal specification and analysis of functional properties of graph rewriting‐based model transformation

Asztalos

Lengyel

Levendovszky

2013

Software Testing Verif & Rel

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SUMMARY Model processing programs are regularly used when working with models or synthetizing the code from them; therefore, their verification has become an essential component of constructing reliable software in model‐based software engineering. Models are usually formalized and visualized as graphs; therefore, model processing programs based on algebraic graph rewriting systems—such programs are called model transformations—are often applied, and their verification has become an important research area. The goal of our research is to support offline transformation analysis by automated methods, where offline means that only the definition of the program itself, the language definitions of its source and target models are used during the analysis. Therefore, the results are independent from concrete source models, and the analysis needs to be performed only once. Based on previous work, this paper provides the synthesis and of a set of individual components and improves them to provide a complete verification solution: (i) a language is introduced to specify the properties to be verified; (ii) a formalism to describe model transformations in a declarative way; and (iii) automated algorithms that can analyse the declarative transformations as well as the properties expressed by the language. Besides its theoretical basis, the implementation of a verification framework is presented, and its operation is illustrated on a case study. Although the formal verification of model transformation properties is algorithmically undecidable in general, our goal is to provide a practically usable, scoped framework that can largely facilitate the manual verification of model transformations. Copyright © 2013 John Wiley & Sons, Ltd.

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Development of Correct Graph Transformation Systems

Cited by 43 publications

References 43 publications

k-Inductive Invariant Checking for Graph Transformation Systems

k-Inductive Invariant Checking for Graph Transformation Systems

Inductive Invariant Checking with Partial Negative Application Conditions

Formal specification and analysis of functional properties of graph rewriting‐based model transformation

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