@book{DyckGiese2015,
  author    = {Dyck, Johannes and Giese, Holger},
  title     = {Inductive invariant checking with partial negative application conditions},
  number    = {98},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-333-6},
  issn      = {1613-5652},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77748},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {43},
  year      = {2015},
  abstract  = {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.},
  language  = {en}
}
@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}
}