Skip to main content
SpringerLink
Log in
Book cover

International Conference on Graph Transformation

ICGT 2019: Graph Transformation pp 93–110Cite as

Unfolding Graph Grammars with Negative Application Conditions

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11629))

Abstract

The unfolding of a graph grammar provides a compact and comprehensive representation of its behaviour, serving both as a semantic model and as the basis for scalable analysis techniques. We study the extension of the theory of unfolding to grammars with negative application conditions (NACs), discuss the challenges with the general case of NACs consisting of complex graph patterns and how they could be avoided by restricting to simpler, incremental NACs.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    For the sake of simplicity we often leave the application of function \(\pi \) implicit.

  2. 2.

    For the sake of conciseness, we depart slightly from [1] by providing the next definition for safe grammars only.

  3. 3.

    Notice that \(Min(\mathcal{O}) \subseteq N_{TG}\; \cup \; E_{TG}\), i.e., it does not contain rules, since the grammar is consuming.

  4. 4.

    We denote a constraint simply as assuming that n is an inclusion.

References

  1. Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Unfolding semantics of graph transformation. Inf. Comput. 205(5), 733–782 (2007)

    Article  MathSciNet  Google Scholar 

  2. Baldan, P., Corradini, A., Heindel, T., König, B., Sobociński, P.: Unfolding grammars in adhesive categories. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 350–366. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03741-2_24

    Chapter  MATH  Google Scholar 

  3. Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Coreflective concurrent semantics for single-pushout graph grammars. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2002. LNCS, vol. 2755, pp. 165–184. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40020-2_9

    Chapter  Google Scholar 

  4. Baldan, P., König, B.: Approximating the behaviour of graph transformation systems. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 14–29. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45832-8_4

    Chapter  MATH  Google Scholar 

  5. Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: an algebraic approach. In: 14th Annual Symposium on Switching and Automata Theory, pp. 167–180. IEEE Computer Society (1973)

    Google Scholar 

  6. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Monographs in Theoretical Computer Science. An EATCS Series. MTCSAES. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31188-2

    Book  MATH  Google Scholar 

  7. Baldan, P., Corradini, A., König, B.: Verifying finite-state graph grammars: an unfolding-based approach. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 83–98. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28644-8_6

    Chapter  Google Scholar 

  8. Qayum, F., Heckel, R.: Search-based refactoring using unfolding of graph transformation systems. ECEASST 38 (2011)

    Google Scholar 

  9. Habel, A., Heckel, R., Taentzer, G.: Graph grammars with negative application conditions. Fundam. Inform. 26(3/4), 287–313 (1996)

    MathSciNet  MATH  Google Scholar 

  10. Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\mathscr {M}\)-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation. MSCS 24(4) (2014)

    Google Scholar 

  11. Ehrig, H., Golas, U., Habel, A., Lambers, L., Orejas, F.: \(\mathscr {M}\)-adhesive transformation systems with nested application conditions. Part 2: embedding, critical pairs and local confluence. Fundam. Inform. 118(1–2), 35–63 (2012)

    MathSciNet  MATH  Google Scholar 

  12. Hermann, F., Corradini, A., Ehrig, H.: Analysis of permutation equivalence in -adhesive transformation systems with negative application conditions. MSCS 24(4) (2014)

    Google Scholar 

  13. Corradini, A., Heckel, R.: Canonical derivations with negative application conditions. In: Giese, H., König, B. (eds.) ICGT 2014. LNCS, vol. 8571, pp. 207–221. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09108-2_14

    Chapter  Google Scholar 

  14. Baldan, P., Busi, N., Corradini, A., Pinna, G.M.: Domain and event structure semantics for Petri nets with read and inhibitor arcs. Theor. Comput. Sci. 323(1–3), 129–189 (2004)

    Article  MathSciNet  Google Scholar 

  15. Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundam. Inform. 26(3/4), 241–265 (1996)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, University of Pisa, Pisa, Italy

    Andrea Corradini

  2. Department of Informatics, University of Leicester, Leicester, UK

    Maryam Ghaffari Saadat & Reiko Heckel

Authors
  1. Andrea Corradini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maryam Ghaffari Saadat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reiko Heckel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Corradini .

Editor information

Editors and Affiliations

  1. Universidad Autónoma de Madrid, Madrid, Spain

    Esther Guerra

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Fernando Orejas

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Corradini, A., Saadat, M.G., Heckel, R. (2019). Unfolding Graph Grammars with Negative Application Conditions. In: Guerra, E., Orejas, F. (eds) Graph Transformation. ICGT 2019. Lecture Notes in Computer Science(), vol 11629. Springer, Cham. https://doi.org/10.1007/978-3-030-23611-3_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-23611-3_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23610-6

  • Online ISBN: 978-3-030-23611-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation