Abstract
We study Petri nets with Reset arcs (also Transfer and Doubling arcs) in combination with other extensions of the basic Petri net model. While Reachability is undecidable in all these extensions (indeed they are Turing-powerful), we exhibit unexpected frontiers for the decidability of Termination, Coverability, Boundedness and place-Boundedness. In particular, we show counter-intuitive separations between seemingly related problems. Our main theorem is the very surprising fact that boundedness is undecidable for Petri nets with Reset arcs.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
P. A. Abdulla, K. čerāns, B. Jonsson, and T. Yih-Kuen. General decidability theorems for infinite-state systems. In Proc. 11th IEEE Symp. Logic in Computer Science (LICS'96), New Brunswick, NJ, USA, July 1996, pages 313–321, 1996.
T. Araki and T. Kasami. Some decision problems related to the reachability problem for Petri nets. Theoretical Computer Science, 3(1):85–104, 1977.
J. Billington. Extensions to coloured Petri nets and their applications to protocols. PhD thesis, University of Cambridge, UK, May 1991. Available as Tech. Report No.222.
G. Ciardo. Petri nets with marking-dependent arc cardinality: Properties and analysis. In Proc. 15th Int. Conf. Applications and Theory of Petri Nets, Zaragoza, Spain, June 1994, volume 815 of Lecture Notes in Computer Science, pages 179–198. Springer-Verlag, 1994.
A. Finkel. Reduction and covering of infinite reachability trees. Information and Computation, 89(2):144–179, 1990.
A. Finkel and Ph. Schnoebelen. Fundamental structures in well-structured infinite transition systems. In Proc. 3rd Latin American Theoretical Informatics Symposium (LATIN'98), Campinas, Brazil, Apr. 1998, volume 1380 of Lecture Notes in Computer Science. Springer-Verlag, 1998.
M. Hack. Decidability questions for Petri nets. PhD Thesis MIT/LCS/TR-161, Massachusetts Institute of Technology, Lab. for Computer Science, June 1976.
M. Kishinevsky, J. Cortadella, A. Kondratyev, L. Lavagno, A. Taubin, and A. Yakovlev. Coupling asynchrony and interrupts: Place chart nets. In Proc. 18th Int. Conf. Application and Theory of Petri Nets, Toulouse, France, June 1997, volume 1248 of Lecture Notes in Computer Science, pages 328–347. Springer-Verlag, 1997.
R. M. Karp and R. E. Miller. Parallel program schemata. Journal of Computer and System Sciences, 3(2):147–195, 1969.
C. Lakos and S. Christensen. A general approach to arc extensions for coloured Petri nets. In Proc. 15th Int. Conf. Applications and Theory of Petri Nets, Zaragoza, Spain, June 1994, volume 815 of Lecture Notes in Computer Science, pages 338–357. Springer-Verlag, 1994.
J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice Hall Int., 1981.
C. Rackoff. The covering and boundedness problems for vector addition systems. Theoretical Computer Science, 6(2):223–231, 1978.
K. Reinhardt. Reachability in Petri nets with inhibitor arcs, November 1995. Unpublished manuscript. See www-fs.informatik.uni-tuebingen.de/~reinhard.
R. Valk. On the computational power of extended Petri nets. In Proc. 7th Symp. Math. Found. Comp. Sci. (MFCS'78), Zakopane, Poland, Sep. 1978, volume 64 of Lecture Notes in Computer Science, pages 526–535, 1978.
R. Valk. Self-modifying nets, a natural extension of Petri nets. In Proc. 5th Int. Coll. Automata, Languages, and Programming (ICALP'78), Udine, Italy, Jul. 1978, volume 62 of Lecture Notes in Computer Science, pages 464–476. Springer-Verlag, 1978.
W. Vogler. Partial order semantics and read arcs. In Proc. 22nd Int. Symp. Math. Found. Comp. Sci. (MFCS'97), Bratislava, Slovakia, Aug. 1997, volume 1295 of Lecture Notes in Computer Science, pages 508–517. Springer-Verlag, 1997.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dufourd, C., Finkel, A., Schnoebelen, P. (1998). Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds) Automata, Languages and Programming. ICALP 1998. Lecture Notes in Computer Science, vol 1443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055044
Download citation
DOI: https://doi.org/10.1007/BFb0055044
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64781-2
Online ISBN: 978-3-540-68681-1
eBook Packages: Springer Book Archive