Synchrony and Asynchrony in Membrane Systems

  • Jetty Kleijn
  • Maciej Koutny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4361)


We consider synchrony and asynchrony in the behavior of various models of membrane systems, which may differ in the way individual reactions are defined as well as in the way multisets of these reactions can be executed in a single computational step. We concentrate on the properties of ongoing computations, including the unbounded ones. Our focus is on the properties of system states involved in such computations as well as on concurrency and causality relationships between executed reactions. This should be contrasted with the approach which investigates different notions of ‘results’ produced through halting computations of membrane systems. As a formal behavioral model we use Petri nets and their processes which are very well suited to capture the notion of an execution in a concurrent context. We continue our earlier work reported in [15], where a systematic and structural link has been established between a basic class of membrane systems and Petri nets. Here, we look at some natural extensions of this basic class of membrane systems and investigate the ways in which they can be represented within the behavioral model provided by Petri nets.


Membrane System Evolution Rule Control Place Reaction Rule Membrane Computing 
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.


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  1. 1.
    Membrane systems web page:
  2. 2.
    Alhazov, A.: Communication in Membrane Systems with Symbol Objects. PhD Thesis, Rovira i Virgili University, Tarragona, Spain (2006)Google Scholar
  3. 3.
    Arroyo, F., Baranda, A.V., Castellanos, J., Păun, G.: Membrane Computing: The Power of (Rule) Creation. Journal of Universal Computer Science 8, 369–381 (2002)Google Scholar
  4. 4.
    Best, E., Devillers, R.: Sequential and Concurrent Behaviour in Petri Net Theory. Theoretical Computer Science 55, 87–136 (1988)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Best, E., Fernández, C.: Nonsequential Processes. A Petri Net View. EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1988)MATHGoogle Scholar
  6. 6.
    Bottoni, P., Martín-Vide, C., Păun, G., Rozenberg, G.: Membrane Systems with Promoters/Inhibitors. Acta Informatica 38, 695–720 (2002)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.): Multiset Processing. LNCS, vol. 2235. Springer, Heidelberg (2001)MATHGoogle Scholar
  8. 8.
    Carloni, L.P., Sangiovanni-Vincentelli, A.L.: A Formal Modelling Framework for Deploying Synchronous Designs on Distributed Architectures. In: Proc. of First International Workshop on Formal Methods for Globally Asynchronous Locally Synchronous Architectures (2003)Google Scholar
  9. 9.
    Dal Zilio, S., Formenti, E.: On the Dynamics of PB Systems: A Petri Net View. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 153–167. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Desel, J., Reisig, W., Rozenberg, G. (eds.): Lectures on Concurrency and Petri Nets. LNCS, vol. 3098. Springer, Heidelberg (2004)MATHGoogle Scholar
  11. 11.
    Freund, R.: Sequential P Systems. Romanian Journal of Information Science and Technology 4, 77–88 (2001)Google Scholar
  12. 12.
    Goltz, U., Reisig, W.: The Non-sequential Behaviour of Petri Nets. Information and Control 57, 125–147 (1983)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kleijn, H.C.M., Koutny, M.: Process Semantics of General Inhibitor Nets. Information and Computation 190, 18–69 (2004)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kleijn, H.C.M., Koutny, M.: Infinite Process Semantics of Inhibitor Nets. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 282–301. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Kleijn, H.C.M., 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)CrossRefGoogle Scholar
  16. 16.
    Kleijn, H.C.M., Koutny, M., Rozenberg, G.: Process Semantics for Membrane Systems. The Journal of Automata, Languages and Combinatorics (to appear, 2006)Google Scholar
  17. 17.
    Kleijn, H.C.M., Koutny, M., Rozenberg, G.: Processes of Petri Nets with Localities. Report 941, School of Computing Science, University of Newcastle (2006)Google Scholar
  18. 18.
    Koutny, M., Pietkiewicz-Koutny, M.: Transition Systems of Elementary Net Systems with Localities. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 173–187. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    McMillan, K.L.: Using Unfoldings to Avoid the State Explosion Problem in the Verification of Asynchronous Circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–174. Springer, Heidelberg (1993)Google Scholar
  20. 20.
    Nielsen, M., Plotkin, G., Winskel, G.: Petri Nets, Event Structures and Domains, Part I. Theoretical Computer Science 13, 85–108 (1980)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 61, 108–143 (2000)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Păun, G.: Computing with Membranes – A Variant. International Journal of Foundations of Computer Science 11, 167–182 (2000)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Păun, G.: Membrane Computing, An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  24. 24.
    Păun, G., Rozenberg, G.: A Guide to Membrane Computing. Theoretical Computer Science 287, 73–100 (2002)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Păun, G., Yu, S.: On Synchronization in P Systems. Fundamenta Informaticae 38, 397–410 (1999)MATHMathSciNetGoogle Scholar
  26. 26.
    Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)Google Scholar
  27. 27.
    Qi, Z., You, J.-y., Mao, H.: P Systems and Petri Nets. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 286–303. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  28. 28.
    Reisig, W., Rozenberg, G. (eds.): APN 1998. LNCS, vol. 1491 and 1492. Springer, Heidelberg (1998)MATHGoogle Scholar
  29. 29.
    Rozenberg, G., Engelfriet, J.: Elementary Net Systems. In: [28], pp. 12–121 (1998)Google Scholar
  30. 30.
    Stahl, C., Reisig, W., Krstić, M.: Hazard Detection in a GALS Wrapper: a Case Study. In: Desel, J., Watanabe, Y. (eds.) ACSD 2005. IEEE Computer Society, Los Alamitos (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jetty Kleijn
    • 1
  • Maciej Koutny
    • 2
  1. 1.LIACSLeiden UniversityLeidenThe Netherlands
  2. 2.School of Computing ScienceUniversity of NewcastleUnited Kingdom

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