Skip to main content
SpringerLink
Log in

Graph Transformation Systems: A Semantics Based on (Stochastic) Symmetric Nets

  • Conference paper
  • First Online:
Dependable Software Engineering. Theories, Tools, and Applications (SETTA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12153))

Abstract

Graph transformation systems (GTS) and Petri nets (PN) are central formal models for concurrent/distributed systems. PN are usually considered as instances of GTS, due to the lack of ability to dynamically adapt their structure. Reversing this perspective, a formal encoding of GTS was recently defined using Symmetric Nets (SN), a High-Level PN formalism which syntactically highlights system behavioural symmetries. This makes it possible reusing the efficient analysis techniques and tools available for SN, e.g., new achievements in SN structural analysis, which are exploited to characterize valid transformation rules. This paper is on the same line, but follows a very different approach. Instead of directly formalizing GTS in terms of SN, a SN semantics is provided for the classical double-pushout approach, by constructively translating DPO rules to equivalent SN subnets. Using the native stochastic extension of SN (SSN) permits a for free encoding of stochastic GTS.

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

Access this chapter

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

Institutional subscriptions

Notes

  1. 1.

    In this paper only unordered classes are used.

  2. 2.

    They can be seen both as bags of functions and bag-functions.

  3. 3.

    Given a transition instance b, we may equivalently write \(b:\ n_i = v_i, \ldots \) or \(n_i(b) = v_i\).

  4. 4.

    L may be seen as a graph whose nodes are \(Var_I \cup Var_{obs}\), and whose edges are represented by the symbolic bag \(bag_{E_L}\).

References

  1. Baarir, S., Beccuti, M., Cerotti, D., De Pierro, M., Donatelli, S., Franceschinis, G.: The GreatSPN tool: recent enhancements. SIGMETRICS Perform. Eval. Rev. 36(4), 4–9 (2009)

    Article  Google Scholar 

  2. Baldan, P., Corradini, A., Gadducci, F., Montanari, U.: From petri nets to graph transformation systems. ECEASST 26, 01 (2010)

    Google Scholar 

  3. Capra, L., De Pierro, M., Franceschinis, G.: Computing structural properties of symmetric nets. In: Campos, J., Haverkort, B.R. (eds.) QEST 2015. LNCS, vol. 9259, pp. 125–140. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22264-6_9

    Chapter  Google Scholar 

  4. Capra, L., De Pierro, M., Franceschinis, G.: A high level language for structural relations in well-formed nets. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 168–187. Springer, Heidelberg (2005). https://doi.org/10.1007/11494744_11

    Chapter  MATH  Google Scholar 

  5. Capra, L.: An operational semantics of graph transformation systems using symmetric nets. Electron. Proc. Theor. Comput. Sci. 303, 107–119 (2019)

    Article  MathSciNet  Google Scholar 

  6. Capra, L., Camilli, M.: Towards evolving Petri nets: a symmetric nets-based framework. IFAC-PapersOnLine 51(7), 480–485 (2018). 14th IFAC Workshop on Discrete Event Systems, WODES 2018

    Article  Google Scholar 

  7. Capra, L., De Pierro, M., Franceschinis, G.: SNexpression: a symbolic calculator for symmetric net expressions. In: Janicki, R., Sidorova, N., Chatain, T. (eds.) PETRI NETS 2020. LNCS, vol. 12152, pp. 381–391. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51831-8_19

    Chapter  Google Scholar 

  8. Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: Stochastic well-formed colored nets and symmetric modeling applications. IEEE Trans. Comput. 42(11), 1343–1360 (1993)

    Article  Google Scholar 

  9. Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: A symbolic reachability graph for coloured Petri nets. Theoret. Comput. Sci. 176(1), 39–65 (1997)

    Article  MathSciNet  Google Scholar 

  10. Corradini, A.: Concurrent graph and term graph rewriting. In: Montanari, U., Sassone, V. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 438–464. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61604-7_69

    Chapter  Google Scholar 

  11. Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic Approaches To Graph Transformation - Part I: Basic Concepts and Double Pushout Approach, pp. 163–245 (1996)

    Google Scholar 

  12. Danos, V., et al.: Graphs, rewriting and pathway reconstruction for rule-based models. In: DŚouza, D., Kavitha, T., Radhakrishnan, J., (eds.) IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2012, Hyderabad, India, vol. 18 of LIPIcs, pp. 276–288 (December 2012). Schloss Dagstuhl Leibniz-Zentrum fuer Informatik

    Google Scholar 

  13. Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.): Handbook of Graph Grammars and Computing by Graph Transformation: Vol. 2: Applications, Languages, and Tools. World Scientific Publishing Co., Inc., USA (1999)

    Google Scholar 

  14. Ehrig, H., Padberg, J.: Graph grammars and Petri net transformations, pp. 496–536 (2003)

    Google Scholar 

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

    Google Scholar 

  16. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, Berlin (2006). https://doi.org/10.1007/3-540-31188-2

    Book  MATH  Google Scholar 

  17. Fokkink, W.: Introduction to Process Algebra. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin (2000). https://doi.org/10.1007/978-3-662-04293-9

    Book  MATH  Google Scholar 

  18. Heckel, R., Lajios, G., Menge, S.: Stochastic graph transformation systems. Fundam. Inform. 74, 63–84 (2004)

    MathSciNet  MATH  Google Scholar 

  19. Jensen, K.: Basic Concepts. Coloured Petri Nets Basic Concepts, Analysis Methods and Practical Use. Monographs in Theoretical Computer Science, vol. 1. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-662-03241-1. 2nd corrected printing. ISBN: 3-540-60943-1, 1997

    Book  MATH  Google Scholar 

  20. Jensen, K., Rozenberg, G. (eds.): High-level Petri Nets: Theory and Application. Springer, London (1991). https://doi.org/10.1007/978-3-642-84524-6

    Book  MATH  Google Scholar 

  21. König, B., Kozioura, V.: Towards the verification of attributed graph transformation systems. In: Ehrig, H., Heckel, R., Rozenberg, G., Taentzer, G. (eds.) ICGT 2008. LNCS, vol. 5214, pp. 305–320. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87405-8_21

    Chapter  MATH  Google Scholar 

  22. Kreowski, H.J.: A comparison between petri-nets and graph grammars. In: Noltemeier, H. (ed.) WG 1980. LNCS, vol. 100. Springer, Heidelberg (1981). https://doi.org/10.1007/3-540-10291-4_22

    Chapter  Google Scholar 

  23. Orejas, F.: Symbolic graphs for attributed graph constraints. J. Symb. Comput. 46(3), 294–315 (2011)

    Article  MathSciNet  Google Scholar 

  24. Padberg, J., Kahloul, L.: Overview of reconfigurable Petri nets, pp. 201–222 (2018)

    Google Scholar 

  25. Reisig, W.: Petri Nets: An Introduction. Monographs in Theoretical Computer Science. An EATCS Series. Springer, New York (1985). https://doi.org/10.1007/978-3-642-69968-9

    Book  MATH  Google Scholar 

  26. Sangiorgi, D., Walker, D.: The \(\pi \)-calculus: a theory of mobile processes. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Milan, Italy

    L. Capra

Authors
  1. L. Capra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Capra .

Editor information

Editors and Affiliations

  1. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Jun Pang

  2. Chinese Academy of Sciences, Beijing, China

    Lijun Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Capra, L. (2020). Graph Transformation Systems: A Semantics Based on (Stochastic) Symmetric Nets. In: Pang, J., Zhang, L. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2020. Lecture Notes in Computer Science(), vol 12153. Springer, Cham. https://doi.org/10.1007/978-3-030-62822-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-62822-2_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62821-5

  • Online ISBN: 978-3-030-62822-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation