@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{SchneiderLambersOrejas2017,
  author    = {Schneider, Sven and Lambers, Leen and Orejas, Fernando},
  title     = {Symbolic model generation for graph properties},
  number    = {115},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  isbn      = {978-3-86956-396-1},
  issn      = {1613-5652},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103171},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {48},
  year      = {2017},
  abstract  = {Graphs are ubiquitous in Computer Science. For this reason, in many areas, it is very important to have the means to express and reason about graph properties. In particular, we want to be able to check automatically if a given graph property is satisfiable. Actually, in most application scenarios it is desirable to be able to explore graphs satisfying the graph property if they exist or even to get a complete and compact overview of the graphs satisfying the graph property. We show that the tableau-based reasoning method for graph properties as introduced by Lambers and Orejas paves the way for a symbolic model generation algorithm for graph properties. Graph properties are formulated in a dedicated logic making use of graphs and graph morphisms, which is equivalent to firstorder logic on graphs as introduced by Courcelle. Our parallelizable algorithm gradually generates a finite set of so-called symbolic models, where each symbolic model describes a set of finite graphs (i.e., finite models) satisfying the graph property. The set of symbolic models jointly describes all finite models for the graph property (complete) and does not describe any finite graph violating the graph property (sound). Moreover, no symbolic model is already covered by another one (compact). Finally, the algorithm is able to generate from each symbolic model a minimal finite model immediately and allows for an exploration of further finite models. The algorithm is implemented in the new tool AutoGraph.},
  language  = {en}
}