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A survey on space complexity of P systems with active membranes

  • Alberto Leporati
  • Luca Manzoni
  • Giancarlo Mauri
  • Antonio E. Porreca
  • Claudio Zandron
Article
  • 63 Downloads

Abstract

P systems with active membranes are a variant of P systems where membranes play an active role during the computation, for example by dividing existing membranes in order to create new ones. In this way, an exponential number of membranes can be obtained in polynomial time, and then used in parallel to attack computationally hard problems. Many interesting questions arise concerning the trade-off between time and space needed to solve various classes of computational problems by means of such membrane systems. In this paper we overview the main results presented in the literature concerning this subject.

Keywords

Membrane computing Computational complexity Space complexity 

References

  1. 1.
    Păun, G.: P systems with active membranes: Attacking NP-complete problems. J. Autom. Lang. Comb. 6(1), 75–90 (2001)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Zandron, C., Ferretti, C., Mauri, G.: Solving NP-complete problems using P systems with active membranes. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds.) Proceedings of the Second International Conference on Unconventional Models of Computation, UMC’2K, pp. 289–301. Springer, New York (2001)CrossRefGoogle Scholar
  3. 3.
    Krishna, S.N., Rama, R.: A variant of P systems with active membranes: solving NP-complete problems. Romanian J. Inf. Sci. Technol. 2(4), 357–367 (1999)Google Scholar
  4. 4.
    Porreca, A.E., Mauri, G., Zandron, C.: Non-confluence in divisionless P systems with active membranes. Theoret. Comput. Sci. 411(6), 878–887 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Sosik, P., Rodriguez-Paton, A.: Membrane computing and complexity theory: a characterization of PSPACE. J. Comput. Syst. Sci. 73, 137–152 (2007)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Simulating elementary active membranes with an application to the P conjecture. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Sosík, P., Zandron, C. (eds.) CMC 2014, LNCS 8961, pp. 284–299. Springer, Heidelberg (2014)Google Scholar
  7. 7.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Membrane division, oracles, and the counting hierarchy. Fundam. Inf. 138(1–2), 97–111 (2015)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: P systems simulating oracle computations. In: Gheorghe, M., Păun, Gh, Salomaa, A., Rozenberg, G., Verlan, S. (eds.) 12th International Conference on Membrane Computing, CMC 2011. Lecture Notes in Computer Science, vol. 7184, pp. 346–358. Springer, New York (2012)Google Scholar
  9. 9.
    Zandron, C., Leporati, A., Ferretti, C., Mauri, G., Perez-Jimenez, M.J.: On the computational efficiency of polarizationless recognizer P systems with strong division and dissolution. Fundam. Inf. 87(1), 79–91 (2008)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Porreca, A.E., Mauri, G., Zandron, C.: Complexity classes for membrane systems. RAIRO-Theor. Inf. Appl. 40(2), 141–162 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: Introducing a space complexity measure for P systems. Int. J. Comput. Commun. Control 4(3), 301–310 (2009)Google Scholar
  12. 12.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: P systems with active membranes: trading time for space. Nat. Comput. 10(1), 167–182 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: P systems with active membranes working in polynomial space. Int. J. Found. Comput. Sci. 22(1), 65–73 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Alhazov, A., Leporati, A., Mauri, G., Porreca, A.E., Zandron, C.: Space complexity equivalence of P systems with active membranes and Turing machines. Theor. Comput. Sci. 529, 69–81 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Porreca, A.E., Leporati, A., Mauri, G., Zandron, C.: Sublinear space P systems with active membranes. In: Membrane Computing: 13th International Conference, CMC: LNCS 7762, vol. 2013, pp. 342–357. Springer, Berlin (2012)CrossRefGoogle Scholar
  16. 16.
    Leporati, A., Mauri, G., Porreca, A.E., Zandron, C.: A gap in the space hierarchy of P systems with active membranes. J. Autom. Lang. Comb. 19(1–4), 173–184 (2014)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Constant-space P systems with active membranes. Fundam. Inf. Fundam. Inf. 134(1–2), 111–128 (2014)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Păun, Gh, Rozenberg, G., Salomaa, A. (eds.): Handbook of Membrane Computing. Oxford University Press, Oxford (2010)zbMATHGoogle Scholar
  19. 19.
    Gheorghe, M., Păun, Gh, Perez-Jimenez, M.J., Rozenberg, G.: Frontiers of membrane computing: open problems and research topics. Intern. J. Found. Comput. Sci. 24(5), 171–250 (2013)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Csuhaj-Varju, E., Oswald, M., Vaszil, Gy.: P automata, handbook of membrane computing. In: Paun, Gh., et al. (eds.), pp. 144–167. Oxford University Press, Oxford (2010)Google Scholar
  21. 21.
    Murphy, N., Woods, D.: The computational power of membrane systems under tight uniformity conditions. Nat. Comput. 10(1), 613–632 (2011)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Boston (1993)zbMATHGoogle Scholar
  23. 23.
    Mix Barrington, D.A., Immerman, N., Straubing, H.: On uniformity within \({\rm NC}^1\). J. Comput. Syst. Sci. 41(3), 274–306 (1990)CrossRefGoogle Scholar
  24. 24.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Trading geometric realism for efficiency in tissue P systems. Romanian J. Inf. Sci. Technol. 19(1–2), 17–30 (2016)Google Scholar
  25. 25.
    Leporati, A., Manzoni, L., Mauri, G., Porreca, A.E., Zandron, C.: Tissue P systems with small cell volume. Fundam. Inf. 154(1–4), 261–275 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Indian Institute of Technology Madras 2018

Authors and Affiliations

  • Alberto Leporati
    • 1
  • Luca Manzoni
    • 1
  • Giancarlo Mauri
    • 1
  • Antonio E. Porreca
    • 1
  • Claudio Zandron
    • 1
  1. 1.Dipartimento di Informatica, Sistemistica e ComunicazioneUniversità degli Studi di Milano-BicoccaMilanoItaly

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