Sequential P Systems with Regular Control

  • Artiom Alhazov
  • Rudolf Freund
  • Hilbert Heikenwälder
  • Marion Oswald
  • Yurii Rogozhin
  • Sergey Verlan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7762)


In this article we introduce the regulating mechanism of control languages for the application of rules assigned to the membranes of a sequential P system and the variant of time-varying sets of rules available at different transition steps. Computational completeness can only be achieved when allowing the system to have no rules applicable for a bounded number of steps; in this case we only need one membrane and periodically available sets of non-cooperative rules, i.e., time-varying sequential P systems. On the other hand, even with an arbitrary number of membranes and regular control languages, only Parikh sets of matrix languages can be obtained if the terminal result has to be taken as soon as the system cannot apply any rule anymore.


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  1. 1.
    Cavaliere, M., Freund, R., Oswald, M., Sburlan, D.: Multiset random context grammars, checkers, and transducers. Theor. Comput. Sci. 372(2-3), 136–151 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Csuhaj-Varjú, E., Dassow, J., Kelemen, J., Păun, G.: Grammar Systems: A Grammatical Approach to Distribution and Cooperation. Gordon and Breach (1994)Google Scholar
  3. 3.
    Dassow, J.: Subregularly controlled derivations: the context-free case. Rostocker Mathematisches Kolloquium 34, 61–70 (1988)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Dassow, J.: Subregularly controlled derivations: restrictions by syntactic parameters. In: Where Mathematics, Computer Science, Linguistics and Biology Meet, pp. 51–61. Kluwer Academic Publishers (2001)Google Scholar
  5. 5.
    Dassow, J.: Subregular restrictions for some language generating devices. In: Freund, R., Holzer, M., Truthe, B., Ultes-Nitsche, U. (eds.) Fourth Workshop on Non-Classical Models for Automata and Applications, NCMA 2012, Fribourg, Switzerland, August 23-24, vol. 290, pp. 11–26 (2012), books@ocg.atGoogle Scholar
  6. 6.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer (1989)Google Scholar
  7. 7.
    Dassow, J., Păun, G., Rozenberg, G.: Grammar systems. In: [18], vol. 2, pp. 155–172 (1997)Google Scholar
  8. 8.
    Dassow, J., Păun, G., Salomaa, A.: Grammars with controlled derivations. In: [18], vol. 2, pp. 101–154 (1997)Google Scholar
  9. 9.
    Fernau, H.: Unconditional transfer in regulated rewriting. Acta Informatica 34(11), 837–857 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Freund, R., Kari, L., Oswald, M., Sosík, P.: Computationally universal P systems without priorities: two catalysts are sufficient. Theor. Comp. Sci. 330, 251–266 (2005)zbMATHCrossRefGoogle Scholar
  11. 11.
    Kudlek, M., Martín-Vide, C., Păun, G.: Toward a Formal Macroset Theory. In: Calude, C.S., Pun, G., Rozenberg, G., Salomaa, A. (eds.) Multiset Processing. LNCS, vol. 2235, pp. 123–134. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Margenstern, M., Rogozhin, Y.: About Time-Varying Distributed H Systems. In: Condon, A., Rozenberg, G. (eds.) DNA 2000. LNCS, vol. 2054, pp. 53–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice Hall (1967)Google Scholar
  14. 14.
    Nielsen, M.: OL systems with control devices. Acta Informatica 4(4), 373–386 (1975)zbMATHCrossRefGoogle Scholar
  15. 15.
    Păun, G.: DNA computing: Distributed Splicing Systems. In: Mycielski, J., Rozenberg, G., Salomaa, A. (eds.) Structures in Logic and Computer Science. LNCS, vol. 1261, pp. 353–370. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Păun, G.: Membrane Computing. An Introduction. Springer (2002)Google Scholar
  17. 17.
    Păun, G., Rozenberg, G., Salomaa, A.: The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  18. 18.
    Rozenberg, G., Salomaa, A.: Handbook of Formal Languages, vol. 3. Springer (1997)Google Scholar
  19. 19.
    Salomaa, A.: On finite automata with a time-variant structure. Information and Control 13(2), 85–98 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Salomaa, A.: Periodically time-variant context-free grammars. Information and Control 17, 294–311 (1970)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    The P Systems Web Page,
  22. 22.
    Verlan, S.: Communicating Distributed H Systems with Alternating Filters. In: Jonoska, N., Păun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 367–384. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Artiom Alhazov
    • 1
    • 4
  • Rudolf Freund
    • 2
  • Hilbert Heikenwälder
    • 2
  • Marion Oswald
    • 2
  • Yurii Rogozhin
    • 1
  • Sergey Verlan
    • 3
  1. 1.Institute of Mathematics and Computer ScienceAcademy of Sciences of MoldovaChişinăuMoldova
  2. 2.Faculty of InformaticsVienna University of TechnologyViennaAustria
  3. 3.LACL, Département InformatiqueUniversité Paris EstCréteilFrance
  4. 4.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly

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