Skip to main content
SpringerLink
Log in

Catalytic Petri Nets Are Turing Complete

  • Conference paper
Book cover Language and Automata Theory and Applications (LATA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7183))

Abstract

In this paper we introduce a class of Petri nets, called catalytic Petri nets, and a suitable firing strategy where transitions are fired only when they use tokens from specific places, called catalytic places. By establishing a one-to-one relationship with catalytic membrane systems, we can prove that the class of catalytic Petri nets with at least two catalytic places is Turing complete.

Work partially supported by the Regione Autonoma della Sardegna; grants L.R. 7/2007 CRP2-120 (Project TESLA) and CRP-17285 (Project TRICS).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Agrigoroaiei, O., Ciobanu, G.: Flattening the Transition P Systems with Dissolution. In: Gheorghe, M., Hinze, T., Păun, G., Rozenberg, G., Salomaa, A. (eds.) CMC 2010. LNCS, vol. 6501, pp. 53–64. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Alberts, B., Johnson, A., Walter, P., Lewis, J.: Molecular Biology of the Cell. Garland Publishing, New York (2002)

    Google Scholar 

  3. Burkhard, H.D.: On Priorities of Parallelism. In: Salwicki, A. (ed.) Logic of Programs 1980. LNCS, vol. 148, pp. 86–97. Springer, Heidelberg (1983)

    Chapter  Google Scholar 

  4. Burkhard, H.D.: Ordered firing in Petri nets. Elektronische Informationsverarbeitung und Kybernetik 17(2/3), 71–86 (1981)

    Google Scholar 

  5. Ciardo, G.: Petri Nets with Marking-Dependent Arc Cardinality: Properties and Analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 179–198. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  6. Ciobanu, G., Pan, L., Păun, G., Pérez-Jiménez, M.J.: P systems with minimal parallelism. Theoretical Computer Science 378(1), 117–130 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  7. Ciobanu, G., Pérez-Jiménez, M.J., Păun, G. (eds.): Applications of Membrane Computing. Natural Computing Series. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  8. Dufourd, C., Finkel, A., Schnoebelen, P.: Reset Nets Between Decidability and Undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  9. Esparza, J.: Decidability and complexity of Petri net problems - an introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Esparza, J., Nielsen, M.: Decidability issues for Petri nets - a survey. Bulletin of the EATCS 52, 244–262 (1994)

    MATH  Google Scholar 

  11. Finkel, A., Geeraerts, G., Raskin, J.F., Begin, L.V.: On the ω-language expressive power of extended Petri nets. Theor. Comput. Sci. 356(3), 374–386 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally universal P systems without priorities: two catalysts are sufficient. Theoretical Computer Science 330(2), 251–266 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Geeraerts, G.: On the expressive power of Petri nets with transfer arcs vs. Petri nets with reset arcs. Tech. Rep. 572, Université Libre de Bruxelles (2007)

    Google Scholar 

  14. Hack, M.: Decidability Questions for Petri Nets. In: Outstanding Dissertations in the Computer Sciences. Garland Publishing, New York (1975)

    Google Scholar 

  15. Jantzen, M., Zetzsche, G.: Labeled Step Sequences in Petri Nets. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 270–287. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  16. Kleijn, J., Koutny, M.: Petri nets and membrane computing. In: Păun, G., Rozenberg, G., Salomaa, A. (eds.) The Oxford Handbook of Membrane Computing, pp. 389–412. Oxford University Press (2010)

    Google Scholar 

  17. Kleijn, J., Koutny, M., Rozenberg, G.: Towards a Petri Net Semantics for Membrane Systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 292–309. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Kosaraju, S.R.: Decidability of reachability in vector addition systems (preliminary version). In: Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pp. 267–281. ACM (1982)

    Google Scholar 

  19. Montanari, U., Rossi, F.: Contextual nets. Acta Informatica 32(6) (1995)

    Google Scholar 

  20. Păun, G.: Membrane Computing. An Introduction. Natural Computing Series. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  21. Păun, G., Rozernberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Romanian Academy, Iaşi, Romania

    Gabriel Ciobanu

  2. Dipartimento di Matematica e Informatica, Università di Cagliari, Italy

    G. Michele Pinna

Authors
  1. Gabriel Ciobanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Michele Pinna
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ciobanu, G., Pinna, G.M. (2012). Catalytic Petri Nets Are Turing Complete. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28332-1_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28331-4

  • Online ISBN: 978-3-642-28332-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation