@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{SchneiderMaximovaGiese2022,
  author    = {Schneider, Sven and Maximova, Maria and Giese, Holger},
  title     = {Invariant Analysis for Multi-Agent Graph Transformation Systems using k-Induction},
  number    = {143},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-531-6},
  issn      = {1613-5652},
  doi       = {10.25932/publishup-54585},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-545851},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {37},
  year      = {2022},
  abstract  = {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.},
  language  = {en}
}