COMPOSITIONAL ANALYSIS FOR REGULARITY, LIVENESS AND BOUNDEDNESS

Li Jiao

Abstract

By the linear algebraic representation of Petri nets, Desel introduced regularity property (Desel, 1992). Regularity implies a sufficient condition for a Petri net to be live and bounded. All the conditions checking the regularity of a Petri net are decidable in polynomial time in the size of a net (Desel and Esparza, 1995). This paper proves that regularity, liveness and boundedness can be preserved after applying many compositional operations to Petri nets. This means that, by applying these compositional operations, a designer can construct complex nets satisfying regularity, liveness and boundedness properties from simpler ones without forward analysis.

References

  1. Berthelot, G., 1986. Checking properties of nets using transformations. In: Rozenberg, G.: LNCS Vol. 222: Advances in Petri nets 1985, pp. 19-40.
  2. Berthelot, G., 1987. Transformations and decompositions of nets. In: Brauer, W.; Reisig, W.; Rozenberg, G., editors: LNCS Vol. 254: Petri Nets: Central Models and Their Properties, Advances in Petri Nets 1986, Part I, Proceedings of an Advanced Course, Bad Honnef, September 1986, pp. 359-376.
  3. Desel, J., 1992. A proof of the rank theorem for extended free choice nets. In Jensen, K., editor: LNCS Vol. 616, Application and Theory of Petri Nets, SpringerVerlag, pp. 134-183.
  4. Desel, J. and Esparza, J., 1995. Free choice Petri nets. London, Cambridge University Press.
  5. Esparza, J. 1994. Reduction and synthesis of live and bounded free choice Petri nets, Information and Computation, Vol. 114, No. 1, pp. 50-87.
  6. Huang, H., Jiao, L. and Cheung, T., 2005. Propertypreserving subnet reductions for designing manufacturing systems with shared resources. Theoretical Computer Science, 332(1-3), pp.461-485.
  7. Koh, I. and DiCesare, F., 1991. Modular transformation methods for generalized Petri nets and their applications in manufacturing automation, IEEE Transactions on Systems, Man and Cybernetics, 21, pp. 963-973.
  8. Recalde, L., Teruel, E. and Silva, M., 1998. On linear algebraic techniques for liveness analysis of P/T systems, Journal of Circuits, Systems, and Computers, 8(1), pp.223-265.
  9. Silva, M., Teruel, E. and Colom, J. M., 1998. Linear algebraic and linear programming techniques for the analysis of Place/Transition net systems, in Reisig, W. and Rozenberg, G., editors: LNCS Vol. 1491, Lectures on Petri Nets I: basic models, Springer-Verlag, pp.309-373.
  10. Souissi, Y., 1991. On liveness preservation by composition of nets via a set of places, In: Rozenberg, G., editor: LNCS Vol. 524, Advances in Petri Nets, pp.277-295.
  11. Suzuki, I. and Murata, T., 1983. A method for stepwise refinement and abstraction of Petri nets, Journal of Computer and System Sciences, 27, pp.51-76.
  12. Valette, R., 1979. Analysis of Petri nets by stepwise refinements, Journal of Computer and System Sciences, 18, pp.35-46.
  13. Zhou, M., 1996. Generalizing parallel and sequential mutual exclusions for Petri net synthesis of manufacturing systems, IEEE Int. Conf. On Emerging Technologies and Factory Automation, 1, pp.49-55.
  14. Zhou, M. and Venkatesh, K., 1999. Modeling, simulation, and control of flexible manufacturing systems: A Petri net approach, World Scientific Publishing Co. Pte.Ltd.
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Paper Citation


in Harvard Style

Jiao L. (2005). COMPOSITIONAL ANALYSIS FOR REGULARITY, LIVENESS AND BOUNDEDNESS . In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO, ISBN 972-8865-30-9, pages 169-174. DOI: 10.5220/0001178901690174


in Bibtex Style

@conference{icinco05,
author={Li Jiao},
title={COMPOSITIONAL ANALYSIS FOR REGULARITY, LIVENESS AND BOUNDEDNESS},
booktitle={Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,},
year={2005},
pages={169-174},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001178901690174},
isbn={972-8865-30-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,
TI - COMPOSITIONAL ANALYSIS FOR REGULARITY, LIVENESS AND BOUNDEDNESS
SN - 972-8865-30-9
AU - Jiao L.
PY - 2005
SP - 169
EP - 174
DO - 10.5220/0001178901690174