@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{MaximovaSchneiderGiese2021,
  author    = {Maximova, Maria and Schneider, Sven and Giese, Holger},
  title     = {Interval probabilistic timed graph transformation systems},
  number    = {134},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-502-6},
  issn      = {1613-5652},
  doi       = {10.25932/publishup-51289},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-512895},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {58},
  year      = {2021},
  abstract  = {The formal modeling and analysis is of crucial importance for software development processes following the model based approach. We present the formalism of Interval Probabilistic Timed Graph Transformation Systems (IPTGTSs) as a high-level modeling language. This language supports structure dynamics (based on graph transformation), timed behavior (based on clocks, guards, resets, and invariants as in Timed Automata (TA)), and interval probabilistic behavior (based on Discrete Interval Probability Distributions). That is, for the probabilistic behavior, the modeler using IPTGTSs does not need to provide precise probabilities, which are often impossible to obtain, but rather provides a probability range instead from which a precise probability is chosen nondeterministically. In fact, this feature on capturing probabilistic behavior distinguishes IPTGTSs from Probabilistic Timed Graph Transformation Systems (PTGTSs) presented earlier. Following earlier work on Interval Probabilistic Timed Automata (IPTA) and PTGTSs, we also provide an analysis tool chain for IPTGTSs based on inter-formalism transformations. In particular, we provide in our tool AutoGraph a translation of IPTGTSs to IPTA and rely on a mapping of IPTA to Probabilistic Timed Automata (PTA) to allow for the usage of the Prism model checker. The tool Prism can then be used to analyze the resulting PTA w.r.t. probabilistic real-time queries asking for worst-case and best-case probabilities to reach a certain set of target states in a given amount of time.},
  language  = {en}
}
@book{MaximovaSchneiderGiese2020,
  author    = {Maximova, Maria and Schneider, Sven and Giese, Holger},
  title     = {Compositional analysis of probabilistic timed graph transformation systems},
  number    = {133},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-501-9},
  issn      = {1613-5652},
  doi       = {10.25932/publishup-49013},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-490131},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {53},
  year      = {2020},
  abstract  = {The analysis of behavioral models is of high importance for cyber-physical systems, as the systems often encompass complex behavior based on e.g. concurrent components with mutual exclusion or probabilistic failures on demand. The rule-based formalism of probabilistic timed graph transformation systems is a suitable choice when the models representing states of the system can be understood as graphs and timed and probabilistic behavior is important. However, model checking PTGTSs is limited to systems with rather small state spaces. We present an approach for the analysis of large scale systems modeled as probabilistic timed graph transformation systems by systematically decomposing their state spaces into manageable fragments. To obtain qualitative and quantitative analysis results for a large scale system, we verify that results obtained for its fragments serve as overapproximations for the corresponding results of the large scale system. Hence, our approach allows for the detection of violations of qualitative and quantitative safety properties for the large scale system under analysis. We consider a running example in which we model shuttles driving on tracks of a large scale topology and for which we verify that shuttles never collide and are unlikely to execute emergency brakes. In our evaluation, we apply an implementation of our approach to the running example.},
  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}
}