Skip to main content
SpringerLink
Log in

A Computational Complexity Theory in Membrane Computing

  • Conference paper
Book cover Membrane Computing (WMC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5957))

Included in the following conference series:

Abstract

In this paper, a computational complexity theory within the framework of Membrane Computing is introduced. Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented. Many attractive characterizations of P ≠ NP conjecture within the framework of a bio-inspired and non-conventional computing model are deduced.

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. Alhazov, A., Pérez–Jiménez, M.J.: Uniform solution of QSAT using polarizationless active membranes. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 122–133. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  2. Alhazov, A., Freund, R., Păun, Gh.: P systems with active membranes and two polarizations. In: Păun, Gh., et al. (eds.) Proc. Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, Sevilla, pp. 20–35 (2004)

    Google Scholar 

  3. Alhazov, A., Pan, L., Păun, G.: Trading polarizations for labels in P systems with active membranes. Acta Informaticae 41(2-3), 111–144 (2004)

    Article  MATH  Google Scholar 

  4. Alhazov, A., Martín–Vide, C., Pan, L.: Solving graph problems by P systems with restricted elementary active membranes. In: Jonoska, N., Păun, Gh., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 1–22. Springer, Heidelberg (2003)

    Google Scholar 

  5. Alhazov, A., Martín–Vide, C., Pan, L.: Solving a PSPACE–complete problem by recognizing P systems with restricted active membranes. Fundamenta Informaticae 58, 67–77 (2003)

    MathSciNet  Google Scholar 

  6. Díaz–Pernil, D., Gutiérrez–Naranjo, M.A., Pérez-Jiménez, M.J., Romero–Jiménez, A.: Efficient simulation of tissue–like P systems by transition cell–like P systems. Natural Computing, http://dx.doi.org/10.1007/s11047-008-9102-z

  7. Díaz–Pernil, D., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Jiménez, A.: Computational efficiency of cellular division in tissue-like membrane systems. Romanian Journal of Information Science and Technology 11(3), 229–241 (2008)

    Google Scholar 

  8. Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-completeness. W.H. Freeman and Company, New York (1979)

    MATH  Google Scholar 

  9. Gutiérrez-Naranjo, R., Pérez-Jiménez, M.J., Rius–Font, M.: Characterizing tractability by tissue–like P systems. In: Gutiérrez–Escudero, R., et al. (eds.) Proc. Seventh Brainstorming Week on Membrane Computing, Fénix Editora, Seville, pp. 169–180 (2009)

    Google Scholar 

  10. 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)

    Article  MATH  Google Scholar 

  11. Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J.: On the power of dissolution in P systems with active membranes. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 224–240. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Gutiérrez–Naranjo, M.A., Pérez–Jiménez, M.J., Riscos–Núñez, A., Romero–Campero, F.J., Romero–Jiménez, A.: Characterizing tractability by cell–like membrane systems. In: Subramanian, K.G., et al. (eds.) Formal Models, Languages and Applications, pp. 137–154. World Scientific, Singapore (2006)

    Google Scholar 

  13. Krishna, S.N., Rama, R.: A variant of P systems with active membranes: Solving NP–complete problems. Romanian Journal of Information Science and Technology 2(4), 357–367 (1999)

    Google Scholar 

  14. Leporati, A., Ferretti, C., Mauri, G., Pérez–Jiménez, M.J., Zandron, C.: Complexity aspects of polarizationless membrane systems. Natural Computing, http://dx.doi.org/10.1007/s11047-008-9100-1

  15. Murphy, N., Woods, D.: Active membrane systems without charges and using only symetric elementary division characterise P. In: Eleftherakis, G., Kefalas, P., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2007. LNCS, vol. 4860, pp. 367–384. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Obtulowicz, A.: Deterministic P systems for solving SAT problem. Romanian Journal of Information Science and Technology 4(1-2), 551–558 (2001)

    MathSciNet  Google Scholar 

  17. Pan, L., Alhazov, A., Ishdorj, T.-O.: Further remarks on P systems with active membranes, separation, merging, and release rules. In: Păun, Gh., et al. (eds.) Proc. Second Brainstorming Week on Membrane Computing, Report RGNC 01/04, Sevilla, pp. 316–324 (2004)

    Google Scholar 

  18. Pan, L., Ishdorj, T.-O.: P systems with active membranes and separation rules. Journal of Universal Computer Science 10(5), 630–649 (2004)

    MathSciNet  Google Scholar 

  19. Pan, L., Pérez-Jiménez, M.J.: Computational complexity of tissue–like P systems with cell separation (submitted, 2009)

    Google Scholar 

  20. Păun, A.: On P systems with membrane division. In: Antoniou, I., et al. (eds.) Unconventional Models of Computation, pp. 187–201. Springer, London (2000)

    Google Scholar 

  21. Păun, Gh.: Computing with membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000); Turku Center for CS-TUCS Report No. 208 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  22. Păun, Gh.: Membrane Computing. An Introduction. Springer, Berlin (2002)

    MATH  Google Scholar 

  23. Păun, Gh.: P systems with active membranes: Attacking NP–complete problems. Journal of Automata, Languages and Combinatorics 6(1), 75–90 (2001)

    MathSciNet  MATH  Google Scholar 

  24. Păun, Gh.: Computing with membranes. Attacking NP–complete problems. In: Antoniou, I., et al. (eds.) Unconventional Models of Computation, pp. 94–115. Springer, London (2000)

    Google Scholar 

  25. Păun, Gh.: Further twenty six open problems in membrane computing. In: Gutiérrez-Naranjo, M.A., et al. (eds.) Proc. Third Brainstorming Week on Membrane Computing, Report RGNC 01/04, Fénix Editora, Sevilla, pp. 249–262 (2005)

    Google Scholar 

  26. Pérez–Jiménez, M.J.: An approach to computational complexity in membrane computing. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 85–109. Springer, Heidelberg (2005)

    Google Scholar 

  27. Pérez-Jiménez, M.J., Riscos-Núñez, A.: Solving the Subset-Sum problem by active membranes. New Generation Computing 23(4), 367–384 (2005)

    Google Scholar 

  28. Pérez-Jiménez, M.J., 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)

    Google Scholar 

  29. Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: A polynomial complexity class in P systems using membrane division. Journal of Automata, Languages and Combinatorics 11(4), 423–434 (2006); A preliminary version in Csuhaj-Varjú, E., et al. (eds.) Proc. Fifth International Workshop on Descriptional Complexity of Formal Systems, DCFS 2003, Budapest, Hungary, July 12-14, pp. 284–294 (2003)

    MathSciNet  MATH  Google Scholar 

  30. Pérez-Jiménez, M.J., Romero–Campero, F.J.: Attacking the common algorithmic problem by recognizer P systems. In: Margenstern, M. (ed.) MCU 2004. LNCS, vol. 3354, pp. 304–315. Springer, Heidelberg (2005)

    Google Scholar 

  31. Pérez–Jiménez, M.J., Romero–Campero, F.J.: An efficient family of P systems for packing items into bins. Journal of Universal Computer Science 10(5), 650–670 (2004)

    MathSciNet  Google Scholar 

  32. Pérez–Jiménez, M.J., Romero-Campero, F.J.: Trading polarizations for bi-stable catalysts in P systems with active membranes. In: Mauri, G., Păun, G., Jesús Pérez-Jímenez, M., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365, pp. 373–388. Springer, Heidelberg (2005)

    Google Scholar 

  33. Pérez–Jiménez, M.J., Romero–Jiménez, A., Sancho–Caparrini, F.: Complexity classes in cellular computing with membranes. Natural Computing 2(3), 265–285 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  34. Porreca, A.E.: Computational Complexity Classes for Membrane Systems, Master Degree Thesis, Universita’ di Milano-Bicocca, Italy (2008)

    Google Scholar 

  35. Porreca, A.E., Mauri, G., Zandron, C.: Complexity classes for membrane systems. Informatique théorique et applications 40(2), 141–162 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Riscos–Núñez, A.: Cellular Programming: efficient resolution of NP–complete numerical problems. PhD. Thesis, University of Sevilla, Spain (2004)

    Google Scholar 

  37. Sosík, P., Rodríguez–Patón, A.: Membrane computing and complexity theory: A characterization of PSPACE. Journal of Computer and System Sciences 73, 137–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  38. Sosík, P.: The computational power of cell division. Natural Computing 2(3), 287–298 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  39. Woods, D., Murphy, N., Pérez-Jiménez, M.J., Riscos-Núñez, A.: Membrane dissolution and division in P. LNCS, vol. 5715, pp. 263–277. Springer, Heidelberg (2009)

    Google Scholar 

  40. 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.) Unconventional Models of Computation, pp. 289–301. Springer, Heidelberg (2000)

    Google Scholar 

  41. Zandron, C., Leporati, A., Ferretti, C., Mauri, G., Pérez–Jiménez, M.J.: On the computational efficiency of polarizationless recognizer P systems with strong division and dissolution. Fundamenta Informaticae 87(1), 79–91 (2008)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, Avda. Reina Mercedes s/n, 41012, Sevilla, Spain

    Mario J. Pérez–Jiménez

Authors
  1. Mario J. Pérez–Jiménez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, PO Box 1-764, 014700, Bucharest, Romania

    Gheorghe Păun

  2. Research Group on Natural Computing, University of Sevilla, Sevilla, Spain

    Mario J. Pérez-Jiménez

  3. Research Group on Natural Computing, University of Sevilla, Spain

    Agustín Riscos-Núñez

  4. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  5. Turku Centre for Computer Science (TUCS), Leminkäisenkatu 14, 20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pérez–Jiménez, M.J. (2010). A Computational Complexity Theory in Membrane Computing. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2009. Lecture Notes in Computer Science, vol 5957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11467-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11467-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11466-3

  • Online ISBN: 978-3-642-11467-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation