Algebraic Higher-Order Nets: Graphs and Petri Nets as Tokens

  • Kathrin Hoffmann
  • Till Mossakowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2755)


Petri nets and Algebraic High-Level Nets are well-known to model parallel and concurrent systems. In this paper, we introduce the concept of Algebraic Higher-Order Nets, which allow to have dynamical tokens like graphs or (ordinary low-level) Petri nets. For this purpose, we specify graphs and Petri nets in the higher-order algebraic specification language HasCasl such that graphs and Petri nets become first-class citizens, i.e. members of algebras (rather than algebras themselves). As an example, we model hospital therapeutic processes by a single higher-order net. Individual care plans for each patient are tokens modeled by low-level nets.


Care Plan Start Stop Patient Care Plan Token Graph EATCS Monograph 
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  1. [ADCR01]
    Agha, G., De Cindio, F., Rozenberg, G. (eds.): APN 2001. LNCS, vol. 2001. Springer, Heidelberg (2001)zbMATHGoogle Scholar
  2. [BH]
    The bremen cofi homepageGoogle Scholar
  3. [CAS99]
    Casl – The CoFI Algebraic Specification Language – Summary, version 1.0. Documents/CASL/Summary. In: [CoF] (July 1999)Google Scholar
  4. [CoF]
    CoFI. The Common Framework Initiative for algebraic specification and development, electronic archives,
  5. [EHKP91]
    Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.): Graph Grammars 1990. LNCS, vol. 532, pp. 269–291. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  6. [EHP+02]
    Ehrig, E., Hoffmann, K., Padberg, J., Baldan, P., Heckel, R.: High Level Net Processes. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 191–219. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  7. [EM85]
    Ehrig, H., Mahr, B.: Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. EATCS Monographs on Theoretical Computer Science, vol. 6. Springer, Berlin (1985)CrossRefzbMATHGoogle Scholar
  8. [EPR94]
    Ehrig, H., Padberg, J., Ribeiro, L.: Algebraic High-Level Nets: Petri Nets Revisited. In: Ehrig, H., Orejas, F. (eds.) Abstract Data Types 1992 and COMPASS 1992. LNCS, vol. 785, pp. 188–206. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  9. [Erm96]
    Ermel, C.: Anforderungsanalyse eines medizinischen Informationssystems mit Algebraischen High-Level-Netzen. Technical Report 96-15, TU Berlin (Masters Thesis TU Berlin) (1996)Google Scholar
  10. [GHP99]
    Gajewsky, M., Hoffmann, K., Padberg, J.: Place Preserving and Transition Gluing Morphisms in Rule-Based Refinement of Place/Transition Systems. Technical Report 99-14, Technical University Berlin (1999)Google Scholar
  11. [Han97]
    Han, Y.: Software Infrastructure for Configurable Workflow System - A Model-Driven Approach Based on Higher-Order Nets and CORBA. PhD thesis, Technical University of Berlin (1997)Google Scholar
  12. [Han00]
    Hannebauer, M.: Autonomous Dynamic Reconfiguration in Collaborative Problem Solving. PhD thesis, Technical University Berlin (2000)Google Scholar
  13. [Hof00]
    Hoffmann, K.: Runtime Modifikation between Algebraic High Level Nets and Algebraic Higher Order Nets using Folding and Unfolding Construction. In: Hommel, G. (ed.) Communication-Based Systems, Proceedings of the 3rd International Workshop, TU Berlin, pp. 55–72. Kluwer Academic Publishers, Dordrecht (2000)CrossRefGoogle Scholar
  14. [PER95]
    Padberg, J., Ehrig, H., Ribeiro, L.: Algebraic high-level net transformation systems. Mathematical Structures in Computer Science 5, 217–256 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Rei85]
    Reisig, W.: Petri Nets. EATCS Monographs on Theoretical Computer Science, vol. 4. Springer, Heidelberg (1985)CrossRefzbMATHGoogle Scholar
  16. [SM02]
    Schröder, L., Mossakowski, T.: HasCasl: Towards integrated specification and development of Haskell programs. In: Kirchner, H., Ringeissen, C. (eds.) AMAST 2002. LNCS, vol. 2422, pp. 99–116. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. [Val98]
    Valk, R.: Petri Nets as Token Objects: An Introduktion to Elementary Object Nets. In: Desel, J., Silva, M. (eds.) ICATPN 1998. LNCS, vol. 1420, pp. 1–25. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  18. [Val00]
    Valk, R.: Concurrency in Communicating Object Petri Nets. In: Agha, G., de Cindio, F., Rozenberg, G. (eds.) Concurrent Object-Oriented Programming and Petri Nets. LNCS, pp. 164–195. Springer, Heidelberg (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kathrin Hoffmann
    • 1
  • Till Mossakowski
    • 2
  1. 1.Institute for Software Engeneering and Theroretical Computer ScienceTechnical University BerlinGermany
  2. 2.BISS, Department of Computer ScienceUniversity of BremenGermany

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