Abstract
In many systems, the values of finitely many parameters can be influenced in a continuous way by controls acting with possibly varying strength over intervals of time. For this, we present general models of continuous Petri nets and of continuous transition systems with situation-dependent concurrency. With a suitable concept of morphisms, we obtain a categorial adjunction between these two models, and often even a coreflection. This shows that the concept of regions is also applicable in this continuous setting. Finally, we prove that our categories of continuous Petri nets and of continuous automata with concurrency have products and conditional coproducts.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Alur, C. Courcoubetis, N. Halbwachs, T. A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, S. Yovine: The algorithmic analysis of hybrid systems Theoretical Computer Science 138 (1995) 3–34.
H. Alla and R. David: Continuous and hybrid Petri nets. Journal of Circuits, Systems and Computers, 8, (1998) 159–188.
E. Badouel and P. Darondeau: Trace nets and process automata. Acta Informatica 32 (1995), 647–679.
E. Badouel and P. Darondeau: Theory of regions in: Third Advanced Course on Petri Nets, Dagstuhl Castle, Lecture Notes in Computer Science vol. 1279, Springer, 1998, 529–586.
R. David and H. Alla: Petri nets for modeling of dynamic systems-a survey. Automatica 30 (1994), 175–202.
E. Dubois, H. Alla and R. David: Continuous Petri net with maximal speeds depending on time. In: 4th Int. Conf. RPI, Computer Integrated Manufacturing and Automation Technology, Troy, USA, Oct. 1994.
I. Demongodin and N. T. Koussoulas: Differential Petri nets: Representing continuous in a discrete-event world. IEEE Trans. on Automatic Control 43 (1998), 573–579.
M. Droste: Concurrent automata and domains. Intern. J. of Found. of Comp. Science 3 (1992), 389–418.
M. Droste and R. M. Shortt: Petri nets and automata with concurrency relations-an adjunction. In: Semantics of Programming Languages and Model Theory (M. Droste, Y. Gurevich, eds.), Gordon and Breach Science Publ., 1993, 69–87.
M. Droste and R.M. Shortt: From Petri nets to automata with concurrency. Applied Categorical Structures, to appear
A. Ehrenfeucht and G. Rozenberg: Partial 2-structures, Acta Informatica 27 (1990), 315–342and 343–368.
M. Mukund: Petri nets and step transition systems. Intern. J. of Found. of Comp. Science 3 (1992), 443–478.
M. Nielsen, G. Rozenberg and P.S. Thiagarajan: Elementary transition systems. Theor. Comp. Science 96 (1992), 3–33.
L. Recalde, E. Teruel and M. Silva: Autonomous continuous P/T systems. In: Proc. 20th Int. Conf. on Applications and Theory of Petri Nets, Lecture Notes in Computer Science, vol. 1639, Springer, 1999, 107–126.
G. Winskel and M. Nielsen: Models for concurrency. In: Handbook of Logic in Computer Science vol. 4 (S. Abramsky, D.M. Gabbay, T.S.E. Maibaum, eds.), Oxford University Press, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Droste, M., Shortt, R.M. (2001). Continuous Petri Nets and Transition Systems. In: Ehrig, H., Padberg, J., Juhás, G., Rozenberg, G. (eds) Unifying Petri Nets. Lecture Notes in Computer Science, vol 2128. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45541-8_14
Download citation
DOI: https://doi.org/10.1007/3-540-45541-8_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43067-4
Online ISBN: 978-3-540-45541-7
eBook Packages: Springer Book Archive