Rule-based refinement of high-level nets preserving safety properties

  • J. Padberg
  • M. Gajewsky
  • C. Ermel
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1382)


The concept of rule-based modification developed in the area of algebraic graph transformations and high-level replacement systems has recently shown to be a powerful concept for vertical stucturing of Petri nets. This includes low-level and high-level Petri nets, especially algebraic high-level nets which can be considered as an integration of algebraic specifications and Petri nets. In a large case study rule-based modification of algebraic high-level nets has been applied successfully for the requirements analysis of a medical information system. The main new result in this paper extends rule-based modification of algebraic highlevel nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rule-based modification of algebraic high-level nets as a vertical development strategy this extension is an important new technique. It is called rule-based refinement. As a running example an important safety property of a medical information system is considered and is shown to be preserved under rule-based refinement.


Petri nets high-level nets algebraic specification safety property rule-based refinement 


  1. [BDH92]
    E. Best, R. Devillers, and J. Hall. The Box Calculus: a new causal algebra with multi-label communication. In Advances in Petri Nets, pages 21–69. Lecture Notes in Computer Science, 1992. 609.Google Scholar
  2. [BGV90]
    W. Brauer, R. Gold, and W. Vogler. A Survey of Behaviour and Equivalence Preserving Refinements of Petri Nets. Advances in Petri Nets, LNCS 483, 1990.Google Scholar
  3. [BS90]
    J. Bradfield and C. Stirling. Verifying temporal properties of processes. In J. C. M. Baeten et al., editors, LNCS; CONCUR'90, Theories of Concurrency: Unification and Extension. (Conference, 1990, Amsterdam, The Netherlands), pages 115–125, Springer, Berlin, 1990.Google Scholar
  4. [CHL95]
    F. Cornelius, H. Hu\mann, and M. Löwe. The Korso Case Study for Software Engineering with Formal Methods: A Medical Information System. In M. Broy and S. JÄhnichen, editors, KORSO: Methods, Languages, and Tools for the Construction of Correct Software, pages 417–445. Springer LNCS 1009, 1995. Also appeared as technical report 94-5, TU Berlin.Google Scholar
  5. [DDGJ90]
    W. Damm, G. Döhmen, V. Gerstner, and B. Josko. Modular verification of petri nets: The temporal logic approach. In J. W. de Bakker et al., editors, LNCS; Proceedings of the REX Workshop on Stepwise Refinement, 1989, Mook, The Netherlands, pages 180–207, Springer, Berlin, 1990.Google Scholar
  6. [DHP91]
    C. Dimitrovici, U. Hummert, and L. Petrucci. Composition and net proper-ties of algebraic high-level nets. In Advances of Petri Nets. Springer Verlag Berlin LNCS 524, 1991.Google Scholar
  7. [DM90]
    J. Desel and A. Meceron. Vincinity Respecting Net Morphisms. In Ad-vances in Petri Nets, pages 165–185. Springer Verlag LNCS 483, 1990.Google Scholar
  8. [EG97]
    C. Ermel and M. Gajewsky. Expanding the Use Of Structuring: Formal Justification for Working on Subnets. In Proceedings of Workshop Petri Nets in System Engineering '97, pages 44-54, University Hamburg, 1997. FBI-HH-B-205/97.Google Scholar
  9. [EHKP91]
    H. Ehrig, A. Habel, H.-J. Kreowski, and F. Parisi-Presicce. Parallelism and concurrency in high-level replacement systems. Math. Struct. in Comp. Science, 1:361–404, 1991.MathSciNetMATHGoogle Scholar
  10. [Ehr79]
    H. Ehrig. Introduction to the algebraic theory of graph grammars. In V. Claus, H. Ehrig, and G. Rozenberg, editors, 1st Graph Grammar Workshop, LNCS 73, pages 1–69. Springer Verlag, 1979.Google Scholar
  11. [EM85]
    H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1: Equa-tions and Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer Verlag, Berlin, 1985.Google Scholar
  12. [EP97]
    H. Ehrig and J. Padberg. Introduction to Universal Parametrized Net Classes. In H. Weber, H. Ehrig, and W. Reisig, editors, MoveOn-Proc. der DFG-Forschergruppe “Petrinetz-Technologie”, Technical Report 97-21, TU Berlin, 1997.Google Scholar
  13. [EPE96]
    C. Ermel, J. Padberg, and H. Ehrig. Requirements Engineering of a Medical Information System Using Rule-Based Refinement of Petri Nets. In D. Cooke, B.J. KrÄmer, P. C-Y. Sheu, J.P. Tsai, and R. Mittermeir, editors, Proc. Integrated Design and Process Technology, pages 186–193. Society for Design and Process Science, 1996. Vol.1.Google Scholar
  14. [Erm96]
    C. Ermel. Anforderungsanalyse eines medizinischen Informationssystems mit Algebraischen High-Level-Netzen. Techn. Report 96-15, TU Berlin, 1996.Google Scholar
  15. [Gen91]
    H.J. Genrich. Predicate/Transition Nets. In High-Level Petri Nets: Theory and Application, pages 3–43. Springer, 1991.Google Scholar
  16. [GG90]
    R.J. van Glabbeck and U. Golz. Equivalences and Refinement. In Semantics of Systems of Concurrent Processes, pages 309–333. Springer, 1990. Lecture Notes in Computer Science 469.Google Scholar
  17. [GL81]
    H.J. Genrich and K. Lautenbach. System modelling with high-level Petri nets. Theoretical Computer Science, 13:109–136, 1981.MathSciNetCrossRefMATHGoogle Scholar
  18. [HRH91]
    R. R. Howell, L. E. Rosier, and Chun Yen Hsu. A taxonomy of fairness and temporal logic problems for petri nets. Theoretical Computer Science, 82(2):341–372, 1991.MathSciNetCrossRefMATHGoogle Scholar
  19. [Hum89]
    U. Hummert. Algebraische High-Level Netze. PhD thesis, Technische Uni-versitÄt Berlin, 1989.Google Scholar
  20. [JCHH91]
    K. Jensen, S. Christensen, P. Huber, and M. Holla. Design/CPN. A Ref-erence Manual. Meta Software Cooperation, 125 Cambridge Park Drive, Cambridge Ma 02140, USA, 1991.Google Scholar
  21. [Jen92]
    K. Jensen. Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, volume 1. Springer, 1992.Google Scholar
  22. [Jen95]
    K. Jensen. Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use, volume 2. Springer, 1995.Google Scholar
  23. [Lil94]
    J. Lilius. On the Structure of High-Level Nets. PhD thesis, Helsinki University of Technology, 1994.Google Scholar
  24. [MP92]
    Zohar Manna and Amir Pnueli. The Temporal Logic of Reactive and Concurrent Systems, Specification. Springer-Verlag, 1992.Google Scholar
  25. [OSS94]
    A. Oberweis, G. Scherrer, and W. Stucky. INCOME/STAR: Methodology and Tools for the Development of Distributed Information Systems. Information Systems, 19(8):643–660, 1994.CrossRefGoogle Scholar
  26. [Pad96]
    J. Padberg. Abstract Petri Nets: A Uniform Approach and Rule-Based Re-finement. PhD thesis, Technical University Berlin, 1996. Shaker Verlag.Google Scholar
  27. [PER95]
    J. Padberg, H. Ehrig, and L. Ribeiro. Algebraic high-level net transforma-tion systems. Math. Struct. in Computer Science, 5:217–256, 1995.MathSciNetCrossRefMATHGoogle Scholar
  28. [Peu97]
    S. Peuker. Invariant property preserving extensions of elementary petri nets. Technical Report No.97–21, TU Berlin, 1997.Google Scholar
  29. [PGE97]
    J. Padberg, M. Gajewsky, and C. Ermel. Refinement versus Verification: Compatibility of Net-Invariants and Stepwise Development of High-Level Petri Nets. Technical Report 97-22, TU Berlin, 1997. to appear.Google Scholar
  30. [Rei91]
    W. Reisig. Petri Nets and Algebraic Specifications. Theoretical Computer Science, 80:1–34, 1991.MATHMathSciNetCrossRefGoogle Scholar
  31. [Sch96]
    K. Schmidt. Symbolische Analysemethoden für algebraische Petri-Netze, volume 4. Bertz Verlag, versal edition, 1996.Google Scholar
  32. [SM97]
    J. Svensson and M. Meier. Handbuch LEU Support-Guide. Vebacom Service GmbH. Also, Scholar
  33. [Vau87]
    Vautherin, J. Parallel System Specification with Coloured Petri Nets. In Rozenberg, G., editor, Advances in Petri Nets 87, pages 293–308. LNCS 266, Springer, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • J. Padberg
    • 1
  • M. Gajewsky
    • 1
  • C. Ermel
    • 1
  1. 1.Technical University of BerlinGermany

Personalised recommendations