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Formal Verification of P Systems with Active Membranes through Model Checking

  • Florentin Ipate
  • Raluca Lefticaru
  • Ignacio Pérez-Hurtado
  • Mario J. Pérez-Jiménez
  • Cristina Tudose
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7184)

Abstract

Formal verification of P systems using model checking has attracted a significant amount of research in recent years. However, up to now only P systems with static structure have been considered. This paper makes significant advances in this area by considering P systems with active membranes, in particular P systems with division rules. The paper presents a theoretical framework for addressing this problem and reports on a complex case study involving a well-known NP-complete problem solved using P systems with membrane division rules. This is implemented in Promela and non trivial properties are verified using Spin.

Keywords

Model Check Linear Temporal Logic Active Membrane Atomic Proposition Kripke Structure 
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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References

  1. 1.
    Andrei, O., Ciobanu, G., Lucanu, D.: Executable Specifications of P Systems. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 126–145. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Ben-Ari, M.: Principles of the Spin Model Checker. Springer, London (2008)MATHGoogle Scholar
  3. 3.
    Bernardini, F., Gheorghe, M., Romero-Campero, F.J., Walkinshaw, N.: A Hybrid Approach to Modeling Biological Systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 138–159. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Ciobanu, G., Pérez-Jiménez, M.J., Păun, G. (eds.): Applications of Membrane Computing. Natural Computing Series. Springer, Heidelberg (2006)MATHGoogle Scholar
  5. 5.
    Clarke Jr., E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Dang, Z., Ibarra, O.H., Li, C., Xie, G.: On Model-Checking of P Systems. In: Calude, C.S., Dinneen, M.J., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 82–93. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Dang, Z., Ibarra, O.H., Li, C., Xie, G.: On the decidability of model-checking for P systems. Journal of Automata, Languages and Combinatorics 11(3), 279–298 (2006)MathSciNetMATHGoogle Scholar
  8. 8.
    Díaz-Pernil, D., Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A Logarithmic Bound for Solving Subset Sum with P Systems. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 257–270. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J., Riscos-Núñez, A.: A fast P system for finding a balanced 2-partition. Soft Computing 9(9), 673–678 (2005)CrossRefMATHGoogle Scholar
  10. 10.
    Ipate, F., Ţurcanu, A.: Modelling, verification and testing of P systems using Rodin and ProB. In: Ninth Brainstorming Week on Membrane Computing (BWMC 2011), pp. 209–220 (2011)Google Scholar
  11. 11.
    Ipate, F., Gheorghe, M., Lefticaru, R.: Test generation from P systems using model checking. Journal of Logic and Algebraic Programming 79(6), 350–362 (2010)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Ipate, F., Lefticaru, R., Tudose, C.: Formal verification of P systems using Spin. International Journal of Foundations of Computer Science 22(1), 133–142 (2011)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Lefticaru, R., Ipate, F., Gheorghe, M.: Model checking based test generation from P systems using P-Lingua. Romanian Journal of Information Science and Technology 13(2), 153–168 (2010)MATHGoogle Scholar
  14. 14.
    P-Lingua website, http://www.p-lingua.org (last visited, November 2011)
  15. 15.
    Pérez-Jiménez, M.J., Jiménez, Á.R., Sancho-Caparrini, F.: Complexity classes in models of cellular computing with membranes. Natural Computing 2(3), 265–285 (2003)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Jesús Pérez-Jímenez, M., Riscos-Núñez, A.: A Linear-time Solution to the Knapsack Problem Using P Systems with Active Membranes. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 250–268. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Pérez-Jiménez, M.J., Riscos-Núñez, A.: Solving the Subset-Sum problem by P systems with active membranes. New Generation Computing 23(4), 339–356 (2005)CrossRefMATHGoogle Scholar
  18. 18.
    Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE (1977)Google Scholar
  19. 19.
    Păun, G.: P systems with active membranes: Attacking NP-complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)MathSciNetMATHGoogle Scholar
  20. 20.
    Păun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002)CrossRefMATHGoogle Scholar
  21. 21.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press (2010)Google Scholar
  22. 22.
    Romero-Campero, F.J., Gheorghe, M., Bianco, L., Pescini, D., Jesús Pérez-Jímenez, M., Ceterchi, R.: Towards Probabilistic Model Checking on P Systems Using PRISM. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 477–495. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Florentin Ipate
    • 1
  • Raluca Lefticaru
    • 1
  • Ignacio Pérez-Hurtado
    • 2
  • Mario J. Pérez-Jiménez
    • 2
  • Cristina Tudose
    • 1
  1. 1.Department of Computer ScienceUniversity of PitestiPitestiRomania
  2. 2.Research Group on Natural Computing, Dept. of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

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