@phdthesis{Dyck2020,
  author    = {Dyck, Johannes},
  title     = {Verification of graph transformation systems with k-inductive invariants},
  doi       = {10.25932/publishup-44274},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-442742},
  school      = {Universit{\"a}t Potsdam},
  pages     = {X, 364},
  year      = {2020},
  abstract  = {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 1970s, graph transformation systems have continuously evolved; related research spans extensions of expressive power, graph algorithms, and their implementation, application scenarios, or verification approaches, to name just a few topics. This thesis focuses on a verification approach for graph transformation systems called k-inductive invariant checking, which is an extension of previous work on 1-inductive invariant checking. Instead of exhaustively computing a system's state space, which is a common approach in model checking, 1-inductive invariant checking symbolically analyzes graph transformation rules - i.e. system behavior - in order to draw conclusions with respect to the validity of graph constraints in the system's state space. The approach is based on an inductive argument: if a system's initial state satisfies a graph constraint and if all rules preserve that constraint's validity, we can conclude the constraint's validity in the system's entire state space - without having to compute it. However, inductive invariant checking also comes with a specific drawback: the locality of graph transformation rules leads to a lack of context information during the symbolic analysis of potential rule applications. This thesis argues that this lack of context can be partly addressed by using k-induction instead of 1-induction. A k-inductive invariant is a graph constraint whose validity in a path of k-1 rule applications implies its validity after any subsequent rule application - as opposed to a 1-inductive invariant where only one rule application is taken into account. Considering a path of transformations then accumulates more context of the graph rules' applications. As such, this thesis extends existing research and implementation on 1-inductive invariant checking for graph transformation systems to k-induction. In addition, it proposes a technique to perform the base case of the inductive argument in a symbolic fashion, which allows verification of systems with an infinite set of initial states. Both k-inductive invariant checking and its base case are described in formal terms. Based on that, this thesis formulates theorems and constructions to apply this general verification approach for typed graph transformation systems and nested graph constraints - and to formally prove the approach's correctness. Since unrestricted graph constraints may lead to non-termination or impracticably high execution times given a hypothetical implementation, this thesis also presents a restricted verification approach, which limits the form of graph transformation systems and graph constraints. It is formalized, proven correct, and its procedures terminate by construction. This restricted approach has been implemented in an automated tool and has been evaluated with respect to its applicability to test cases, its performance, and its degree of completeness.},
  language  = {en}
}
@book{DyckGiese2017,
  author    = {Dyck, Johannes and Giese, Holger},
  title     = {k-Inductive invariant checking for graph transformation systems},
  number    = {119},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-406-7},
  issn      = {1613-5652},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-397044},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {45},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}
@book{DyckGieseLambers2017,
  author    = {Dyck, Johannes and Giese, Holger and Lambers, Leen},
  title     = {Automatic verification of behavior preservation at the transformation level for relational model transformation},
  number    = {112},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-391-6},
  issn      = {1613-5652},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100279},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {viii, 112},
  year      = {2017},
  abstract  = {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.},
  language  = {en}
}