Skip to main content

Transformations in Reconfigurable Place/Transition Systems

  • Chapter
Book cover Concurrency, Graphs and Models

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5065))

Abstract

Reconfigurable place/transition systems are Petri nets with initial markings and a set of rules which allow the modification of the net during runtime in order to adapt the net to new requirements. For the transformation of Petri nets in the double pushout approach, the categorical framework of adhesive high-level replacement systems has been instantiated to Petri nets. In this paper, we show that also place/transition systems form a weak adhesive high-level replacement category. This allows us to apply the developed theory also to tranformations within reconfigurable place/transition systems.

This work has been partly funded by the research project for MANET of the German Research Council (see http://tfs.cs.tu-berlin.de/formalnet/).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Meseguer, J., Montanari, U.: Petri Nets are Monoids. Information and Computation 88(2), 105–155 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  2. Hoffmann, K., Ehrig, H., Mossakowski, T.: High-Level Nets with Nets and Rules as Tokens. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 268–288. Springer, Heidelberg (2005)

    Google Scholar 

  3. Ehrig, H., Hoffmann, K., Padberg, J., Prange, U., Ermel, C.: Independence of Net Transformations and Token Firing in Reconfigurable Place/Transition Systems. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 104–123. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. EATCS Monographs. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  5. Ehrig, H., Habel, A., Padberg, J., Prange, U.: Adhesive High-Level Replacement Systems: A New Categorical Framework for Graph Transformation. Fundamenta Informaticae 74(1), 1–29 (2006)

    MATH  MathSciNet  Google Scholar 

  6. Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation: Foundations, vol. 1. World Scientific, Singapore (1997)

    MATH  Google Scholar 

  7. Lack, S., Sobociński, P.: Adhesive and Quasiadhesive Categories. Theoretical Informatics and Applications 39(3), 511–546 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Prange, U.: Algebraic High-Level Nets as Weak Adhesive HLR Categories. Electronic Communications of the EASST 2, 1–13 (2007)

    Google Scholar 

  9. Reisig, W.: Petri Nets. EATCS Monographs on Theoretical Computer Science, vol. 4. Springer, Berlin (1985)

    MATH  Google Scholar 

  10. Nielsen, M., Rozenberg, G., Thiagarajan, P.S.: Elementary Transition Systems. Theoretical Computer Science 96(1), 3–33 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars (A Survey). In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)

    Chapter  Google Scholar 

  12. Billington, J.: Extensions to Coloured Petri Nets. In: Proceedings of PNPM 1989, pp. 61–70. IEEE, Los Alamitos (1989)

    Google Scholar 

  13. Campos, J., Sánchez, B., Silva, M.: Throughput Lower Bounds for Markovian Petri Nets: Transformation Techniques. In: Proceedings of PNPM 1991, pp. 322–331. IEEE, Los Alamitos (1991)

    Google Scholar 

  14. Urbášek, M.: Categorical Net Transformations for Petri Net Technology. PhD thesis, TU Berlin (2003)

    Google Scholar 

  15. Belli, F., Dreyer, J.: Systems Modelling and Simulation by Means of Predicate/Transition Nets and Logic Programming. In: Proceedings of IEA/AIE 1994, pp. 465–474 (1994)

    Google Scholar 

  16. Bessey, T., Becker, M.: Comparison of the Modeling Power of Fluid Stochastic Petri Nets (FSPN) and Hybrid Petri Nets (HPN). In: Proceedings of SMC 2002, vol. 2, pp. 354–358. IEEE, Los Alamitos (2002)

    Google Scholar 

  17. de Lara, J., Vangheluwe, H.: Computer Aided Multi-Paradigm Modelling to Process Petri-Nets and Statecharts. In: Corradini, A., Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) ICGT 2002. LNCS, vol. 2505, pp. 239–253. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Kluge, O.: Modelling a Railway Crossing with Message Sequence Charts and Petri Nets. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 197–218. Springer, Heidelberg (2003)

    Google Scholar 

  19. Parisi-Presicce, F.: A Formal Framework for Petri Net Class Transformations. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 409–430. Springer, Heidelberg (2003)

    Google Scholar 

  20. Corts, L., Eles, P., Peng, Z.: Modeling and Formal Verification of Embedded Systems Based on a Petri Net Representation. Journal of Systems Architecture 49(12-15), 571–598 (2003)

    Article  Google Scholar 

  21. Haddad, S.: A Reduction Theory for Coloured Nets. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 209–235. Springer, Heidelberg (1990)

    Google Scholar 

  22. Desel, J.: On Abstraction of Nets. In: Rozenberg, G. (ed.) APN 1991. LNCS, vol. 524, pp. 78–92. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  23. Esparza, J., Silva, M.: On the Analysis and Synthesis of Free Choice Systems. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 243–286. Springer, Heidelberg (1991)

    Google Scholar 

  24. Chehaibar, G.: Replacement of Open Interface Subnets and Stable State Transformation Equivalence. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 1–25. Springer, Heidelberg (1993)

    Google Scholar 

  25. Bonhomme, P., Aygalinc, P., Berthelot, G., Calvez, S.: Hierarchical Control of Time Petri Nets by Means of Transformations. In: Proceedings of SMC 2002, vol. 4, pp. 6–11. IEEE Computer Society Press, Los Alamitos (2002)

    Google Scholar 

  26. Berthelot, G.: Checking Properties of Nets Using Transformation. In: Rozenberg, G. (ed.) APN 1985. LNCS, vol. 222, pp. 19–40. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  27. Berthelot, G.: Transformations and Decompositions of Nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 359–376. Springer, Heidelberg (1987)

    Google Scholar 

  28. Best, E., Thielke, T.: Orthogonal Transformations for Coloured Petri Nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 447–466. Springer, Heidelberg (1997)

    Google Scholar 

  29. Murata, T.: Petri Nets: Properties, Analysis and Applications. In: Proceedings of the IEEE, vol. 77, pp. 541–580. IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  30. Best, E., Devillers, R., Koutny, M.: The Box Algebra = Petri Nets + Process Expressions. Information and Computation 178(1), 44–100 (2002)

    MATH  MathSciNet  Google Scholar 

  31. van der Aalst, W.: The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems and Computers 8(1), 21–66 (1998)

    Article  Google Scholar 

  32. Padberg, J., Gajewsky, M., Ermel, C.: Rule-based Refinement of High-Level Nets Preserving Safety Properties. Science of Computer Programming 40(1), 97–118 (2001)

    Article  MATH  Google Scholar 

  33. Padberg, J., Urbášek, M.: Rule-Based Refinement of Petri Nets: A Survey. In: Ehrig, H., Reisig, W., Rozenberg, G., Weber, H. (eds.) Petri Net Technology for Communication-Based Systems. LNCS, vol. 2472, pp. 161–196. Springer, Heidelberg (2003)

    Google Scholar 

  34. Baldan, P., Corradini, A., Ehrig, H., Heckel, R., König, B.: Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets. In: Mossakowski, T., Montanari, U., Haveraaen, M. (eds.) CALCO 2007. LNCS, vol. 4624, pp. 126–142. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  35. Balbo, G., Bruell, S., Sereno, M.: Product Form Solution for Generalized Stochastic Petri Nets. IEEE Transactions on Software Engineering 28(10), 915–932 (2002)

    Article  Google Scholar 

  36. Carmona, J., Cortadella, J.: Input/Output Compatibility of Reactive Systems. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 360–377. Springer, Heidelberg (2002)

    Google Scholar 

  37. Cheung, T., Lu, Y.: Five Classes of Invariant-Preserving Transformations on Colored Petri Nets. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 384–403. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  38. Esparza, J.: Model Checking Using Net Unfoldings. Science of Computer Programming 23(2-3), 151–195 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  39. Padberg, J., Hoffmann, K., Ehrig, H., Modica, T., Biermann, E., Ermel, C.: Maintaining Consistency in Layered Architectures of Mobile Ad-hoc Networks. In: Dwyer, M.B., Lopes, A. (eds.) FASE 2007. LNCS, vol. 4422, pp. 383–397. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  40. Llorens, M., Oliver, J.: Structural and Dynamic Changes in Concurrent Systems: Reconfigurable Petri Nets. IEEE Transactions on Computers 53(9), 1147–1158 (2004)

    Article  Google Scholar 

  41. AGG Homepage (2007), http://tfs.cs.tu-berlin.de/agg

  42. Kindler, E., Weber, M.: The Petri Net Kernel - An Infrastructure for Building Petri Net Tools. Software Tools for Technology Transfer 3(4), 486–497 (2001)

    MATH  Google Scholar 

  43. Lambers, L., Ehrig, H., Prange, U., Orejas, F.: Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions. Electronic Notes in Theoretical Computer Science (to appear 2008)

    Google Scholar 

  44. Padberg, J., Ehrig, H., Ribeiro, L.: Algebraic High-Level Net Transformation Systems. Mathematical Structures in Computer Science 5(2), 217–256 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  45. Prange, U.: Algebraic High-Level Systems as Weak Adhesive HLR Categories. Electronic Notes in Theoretical Computer Science (to appear, 2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Pierpaolo Degano Rocco De Nicola José Meseguer

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Prange, U., Ehrig, H., Hoffmann, K., Padberg, J. (2008). Transformations in Reconfigurable Place/Transition Systems. In: Degano, P., De Nicola, R., Meseguer, J. (eds) Concurrency, Graphs and Models. Lecture Notes in Computer Science, vol 5065. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68679-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68679-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68676-7

  • Online ISBN: 978-3-540-68679-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics