Abstract
Discrete event dynamic systems may have extremely large state spaces. For their analysis, it is usual to relax the description by removing the integrality constraints. Applying this idea, continuous P/T systems are defined by allowing fractional firings of transitions, and thus the existence of non-discrete markings [4,5,1]. In this paper we compare the behaviors of discrete and continuous systems, and observe that they are not necessarily similar. The problems that appear lead to the definition of two extensions of reachability. Many properties shall be extended differently depending on which reachability definition is being considered. Here, we concentrate on liveness and deadlock-freeness, proposing extensions and relating them to their discrete counterparts.
This work was partially supported by the project HF97-169, within the Picasso programme and project CICYT TAP98-0679
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Alla and R. David. Continuous and hybrid Petri nets. Journal of Circuits, Systems, and Computers, 8(1), 1998.
R. Champagnat, P. Esteban, H. Pingaud, and R. Valette. Modeling hybrid systems through by means of high-level Petri nets. benefits and limitations. In M. Ferney, P. Borne, A. El Moudni, and L. Grujic, editors, Proceedings of CIS’97, volume 1, pages 469–474, Belfort, France, 1997.
R. Champagnat, H. Pingaud, H. Alla, C. Valentin-Roubinet, and J.M. Flaus. A gas storage example as a benchmark for hybrid modelling. In Proc. of ADPM’98, pages 123–130, Reims, France, March 1998.
R. David and H. Alla. Continuous Petri nets. In Proc. of the 8th European Workshop on Application and Theory of Petri Nets, pages 275–294, Zaragoza, Spain, 1987.
R. David and H. Alla. Autonomous and timed continuous Petri nets. In Rozenberg [10], pages 71–90.
J. Desel and J. Esparza. Free Choice Petri Nets, volume 40 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1995.
J. Ezpeleta, J.M. Couvreur, and M. Silva. A new technique for finding a generating family of siphons, traps and ST-components. application to coloured Petri nets. In Rozenberg [10], pages 126–147.
D. G. Luenberger. Introduction to Linear and non Linear Programming. Addison-Wesley Publishing Company, 1972.
L. Recalde, E. Teruel, and M. Silva. On linear algebraic techniques for liveness analysis of P/T systems. Journal of Circuits, Systems, and Computers, 8(1):223–265, 1998.
G. Rozenberg, editor. Advances in Petri Nets 1993, volume 674 of Lecture Notes in Computer Science. Springer, 1993.
M. Silva. Towards a synchrony theory for P/T nets. In K. Voss et al., editors, Concurrency and Nets, pages 435–460. Springer, 1987.
M. Silva, E. Teruel, and J. M. Colom. Linear algebraic techniques for the analysis of net systems. In G. Rozenberg and W. Reisig, editors, Advances in Petri Nets, Lecture Notes in Computer Science. Springer, 1998. To appear.
E. Teruel and M. Silva. Structure theory of equal conflict systems. Theoretical Computer Science, 153(1-2):271–300, 1996.
K. Trivedi and V. G. Kulkarni. FSPNs: Fluid stochastic Petri nets. In M. Ajmone Marsan, editor, Application and Theory of Petri Nets 1993, volume 691 of Lecture Notes in Computer Science, pages 24–31. Springer, 1993.
C. Valentin and P. Ladet. Flow modelling in a class of hybrid (continuous/discrete) systems. In IEEE Int. Conf. on Systems, Man, and Cybernetics, Le Touquet, France, October 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Recalde, L., Teruel, E., Silva, M. (1999). Autonomous Continuous P/T Systems. In: Donatelli, S., Kleijn, J. (eds) Application and Theory of Petri Nets 1999. ICATPN 1999. Lecture Notes in Computer Science, vol 1639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48745-X_8
Download citation
DOI: https://doi.org/10.1007/3-540-48745-X_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66132-0
Online ISBN: 978-3-540-48745-6
eBook Packages: Springer Book Archive