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k-Inductive invariant checking for graph transformation systems

Author: Dyck, Johannes

Publisher: Universitätsverlag Potsdam

Published: 2017-09-15

Total Pages: 52

ISBN-13: 3869564067

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.

Invariant Analysis for Multi-Agent Graph Transformation Systems using k-Induction

Author: Sven Schneider

Publisher: Universitätsverlag Potsdam

Published: 2022-11-17

Total Pages: 44

ISBN-13: 3869565314

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The analysis of behavioral models such as Graph Transformation Systems (GTSs) is of central importance in model-driven engineering. However, GTSs often result in intractably large or even infinite state spaces and may be equipped with multiple or even infinitely many start graphs. To mitigate these problems, static analysis techniques based on finite symbolic representations of sets of states or paths thereof have been devised. We focus on the technique of k-induction for establishing invariants specified using graph conditions. To this end, k-induction generates symbolic paths backwards from a symbolic state representing a violation of a candidate invariant to gather information on how that violation could have been reached possibly obtaining contradictions to assumed invariants. However, GTSs where multiple agents regularly perform actions independently from each other cannot be analyzed using this technique as of now as the independence among backward steps may prevent the gathering of relevant knowledge altogether. In this paper, we extend k-induction to GTSs with multiple agents thereby supporting a wide range of additional GTSs. As a running example, we consider an unbounded number of shuttles driving on a large-scale track topology, which adjust their velocity to speed limits to avoid derailing. As central contribution, we develop pruning techniques based on causality and independence among backward steps and verify that k-induction remains sound under this adaptation as well as terminates in cases where it did not terminate before.

Inductive invariant checking with partial negative application conditions

Author: Dyck, Johannes

Publisher: Universitätsverlag Potsdam

Published: 2016-04-13

Total Pages: 48

ISBN-13: 3869563338

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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 report 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.

Verification of Graph Transformation Systems with K-inductive Invariants

Author: Johannes Dyck

Publisher:

Published: 2019*

Total Pages:

ISBN-13:

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With rising complexity of today's software and hardware systems and the hypothesized increase in autonomous, intelligent, and self-* systems, developing correct systems remains an important challenge. Testing, although an important part of the development and maintainance process, cannot usually establish the definite correctness of a software or hardware system - especially when systems have arbitrarily large or infinite state spaces or an infinite number of initial states. This is where formal verification comes in: given a representation of the system in question in a formal framework, verification approaches and tools can be used to establish the system's adherence to its similarly formalized specification, and to complement testing. One such formal framework is the field of graphs and graph transformation systems. Both are powerful formalisms with well-established foundations and ongoing research that can be used to describe complex hardware or software systems with varying degrees of abstraction. Since their inception in the ...

Automatic verification of behavior preservation at the transformation level for relational model transformation

Author: Dyck, Johannes

Publisher: Universitätsverlag Potsdam

Published: 2017-04-26

Total Pages: 126

ISBN-13: 3869563915

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The correctness of model transformations is a crucial element for model-driven engineering of high quality software. In particular, behavior preservation is the most important correctness property avoiding the introduction of semantic errors during the model-driven engineering process. Behavior preservation verification techniques either show that specific properties are preserved, or more generally and complex, they show some kind of behavioral equivalence or refinement between source and target model of the transformation. Both kinds of behavior preservation verification goals have been presented with automatic tool support for the instance level, i.e. for a given source and target model specified by the model transformation. However, up until now there is no automatic verification approach available at the transformation level, i.e. for all source and target models specified by the model transformation. In this report, we extend our results presented in [27] and outline a new sophisticated approach for the automatic verification of behavior preservation captured by bisimulation resp. simulation for model transformations specified by triple graph grammars and semantic definitions given by graph transformation rules. In particular, we show that the behavior preservation problem can be reduced to invariant checking for graph transformation and that the resulting checking problem can be addressed by our own invariant checker even for a complex example where a sequence chart is transformed into communicating automata. We further discuss today's limitations of invariant checking for graph transformation and motivate further lines of future work in this direction.

Graph Transformation

Author: Fabio Gadducci

Publisher: Springer Nature

Published: 2020-06-25

Total Pages: 346

ISBN-13: 3030513726

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This book constitutes the refereed proceedings of the 13th International Conference on Graph Transformation, ICGT 2020, in Bergen, Norway, in June 2020.* The 16 research papers and 4 tool paper presented in this book were carefully reviewed and selected from 40 submissions. One invited paper is also included. The papers deal with the following topics: theoretical advances; application domains; and tool presentations. *The conference was held virtually due to the COVID-19 pandemic.

Modeling and Formal Analysis of Meta-Ecosystems with Dynamic Structure using Graph Transformation

Author: Boris Flotterer

Publisher: Universitätsverlag Potsdam

Published: 2023-01-08

Total Pages: 54

ISBN-13: 3869565330

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The dynamics of ecosystems is of crucial importance. Various model-based approaches exist to understand and analyze their internal effects. In this paper, we model the space structure dynamics and ecological dynamics of meta-ecosystems using the formal technique of Graph Transformation (short GT). We build GT models to describe how a meta-ecosystem (modeled as a graph) can evolve over time (modeled by GT rules) and to analyze these GT models with respect to qualitative properties such as the existence of structural stabilities. As a case study, we build three GT models describing the space structure dynamics and ecological dynamics of three different savanna meta-ecosystems. The first GT model considers a savanna meta-ecosystem that is limited in space to two ecosystem patches, whereas the other two GT models consider two savanna meta-ecosystems that are unlimited in the number of ecosystem patches and only differ in one GT rule describing how the space structure of the meta-ecosystem grows. In the first two GT models, the space structure dynamics and ecological dynamics of the meta-ecosystem shows two main structural stabilities: the first one based on grassland-savanna-woodland transitions and the second one based on grassland-desert transitions. The transition between these two structural stabilities is driven by high-intensity fires affecting the tree components. In the third GT model, the GT rule for savanna regeneration induces desertification and therefore a collapse of the meta-ecosystem. We believe that GT models provide a complementary avenue to that of existing approaches to rigorously study ecological phenomena.

Metric Temporal Graph Logic over Typed Attributed Graphs

Author: Holger Giese

Publisher: Universitätsverlag Potsdam

Published: 2018

Total Pages: 36

ISBN-13: 3869564334

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Various kinds of typed attributed graphs are used to represent states of systems from a broad range of domains. For dynamic systems, established formalisms such as graph transformations provide a formal model for defining state sequences. We consider the extended case where time elapses between states and introduce a logic to reason about these sequences. With this logic we express properties on the structure and attributes of states as well as on the temporal occurrence of states that are related by their inner structure, which no formal logic over graphs accomplishes concisely so far. Firstly, we introduce graphs with history by equipping every graph element with the timestamp of its creation and, if applicable, its deletion. Secondly, we define a logic on graphs by integrating the temporal operator until into the well-established logic of nested graph conditions. Thirdly, we prove that our logic is equally expressive to nested graph conditions by providing a suitable reduction. Finally, the implementation of this reduction allows for the tool-based analysis of metric temporal properties for state sequences. Verschiedene Arten von getypten attributierten Graphen werden benutzt, um Zustände von Systemen in vielen unterschiedlichen Anwendungsbereichen zu beschreiben. Der etablierte Formalismus der Graphtransformationen bietet ein formales Model, um Zustandssequenzen für dynamische Systeme zu definieren. Wir betrachten den erweiterten Fall von solchen Sequenzen, in dem Zeit zwischen zwei verschiedenen Systemzuständen vergeht, und führen eine Logik ein, um solche Sequenzen zu beschreiben. Mit dieser Logik drücken wir zum einen Eigenschaften über die Struktur und die Attribute von Zuständen aus und beschreiben zum anderen temporale Vorkommen von Zuständen, die durch ihre innere Struktur verbunden sind. Solche Eigenschaften können bisher von keiner der existierenden Logiken auf Graphen vergleichbar darstellt werden. Erstens führen wir Graphen mit Änderungshistorie ein, indem wir jedes Graphelement mit einem Zeitstempel seiner Erzeugung und, wenn nötig, seiner Löschung versehen. Zweitens definieren wir eine Logik auf Graphen, indem wir den Temporaloperator Until in die wohl-etablierte Logik der verschachtelten Graphbedingungen integrieren. Drittens beweisen wir, dass unsere Logik gleich ausdrucksmächtig ist, wie die Logik der verschachtelten Graphbedingungen, indem wir eine passende Reduktionsoperation definieren. Zuletzt erlaubt uns die Implementierung dieser Reduktionsoperation die werkzeukbasierte Analyse von metrisch-temporallogischen Eigenschaften für Zustandssequenzen zu führen.

Towards version control in object-based systems

Author: Jakob Reschke

Publisher: Universitätsverlag Potsdam

Published: 2018

Total Pages: 106

ISBN-13: 386956430X

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Version control is a widely used practice among software developers. It reduces the risk of changing their software and allows them to manage different configurations and to collaborate with others more efficiently. This is amplified by code sharing platforms such as GitHub or Bitbucket. Most version control systems track files (e.g., Git, Mercurial, and Subversion do), but some programming environments do not operate on files, but on objects instead (many Smalltalk implementations do). Users of such environments want to use version control for their objects anyway. Specialized version control systems, such as the ones available for Smalltalk systems (e.g., ENVY/Developer and Monticello), focus on a small subset of objects that can be versioned. Most of these systems concentrate on the tracking of methods, classes, and configurations of these. Other user-defined and user-built objects are either not eligible for version control at all, tracking them involves complicated workarounds, or a fixed, domain-unspecific serialization format is used that does not equally suit all kinds of objects. Moreover, these version control systems that are specific to a programming environment require their own code sharing platforms;popular, well-established platforms for file-based version control systems cannot be used or adapter solutions need to be implemented and maintained. To improve the situation for version control of arbitrary objects, a framework for tracking, converting, and storing of objects is presented in this report. It allows editions of objects to be stored in an exchangeable, existing backend version control system. The platforms of the backend version control system can thus be reused. Users and objects have control over how objects are captured for the purpose of version control. Domain-specific requirements can be implemented. The storage format (i.e. the file format, when file-based backend version control systems are used) can also vary from one object to another. Different editions of objects can be compared and sets of changes can be applied to graphs of objects. A generic way for capturing and restoring that supports most kinds of objects is described. It models each object as a collection of slots. Thus, users can begin to track their objects without first having to implement version control supplements for their own kinds of objects. The proposed architecture is evaluated using a prototype implementation that can be used to track objects in Squeak/Smalltalk with Git. The prototype improves the suboptimal standing of user objects with respect to version control described above and also simplifies some version control tasks for classes and methods as well. It also raises new problems, which are discussed in this report as well.

Graph Transformation

Author: Juan de Lara

Publisher: Springer

Published: 2017-07-03

Total Pages: 239

ISBN-13: 3319614703

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This book constitutes the refereed proceedings of the 10th International Conference on Graph Transformation, ICGT 2017, held as part of STAF 2017, in Marburg, Germany, in July 2017. The 14 papers presented were carefully reviewed and selected from 23 submissions. The papers cover a wide range of topics including theoretical approaches to graph transformation and their verification, model-driven engineering, chemical reactions as well as various applications. They are organized in the following topical sections: foundations; graph language and parsing; analysis and verification; and model transformation and tools.