Skip to main content
SpringerLink
Log in

A Uniform Family of Tissue P Systems with Protein on Cells Solving 3-Coloring in Linear Time

  • Conference paper
  • First Online:
Unconventional Computation and Natural Computation (UCNC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9252))

  • 670 Accesses

Abstract

A new variant of tissue P systems called tissue P system with protein on cells is used in this paper. It has the ability to move proteins between cells. It is inspired from the biology that the cells communicate by sending and receiving signals. Signals most often move through the cell by passing from protein to protein. In tissue P systems with protein on cells, multisets of objects together with proteins between cells are exchanged. We present in this paper a linear solution of the 3-coloring problem, a well known NP-complete problem. In this new variant, these objects called proteins are used to obtain a new solution where the number of rules is lesser than that appears in the original solution with tissue P systems. The number of steps to obtain the solution is lesser than the conventional tissue P system. This is a strong point when someone wants to implement a solution in a practical way.

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 EPUB and 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

References

  1. Alhazov, A., Freund, R., Oswald, M.: Tissue P systems with antiport rules and small numbers of symbols and cells. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 100–111. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Appel, K., Haken, W.: Every planar map is 4-colorable - 1: Discharging. Ill. J. Math. 21, 429–490 (1977)

    MathSciNet  MATH  Google Scholar 

  3. Appel, K., Haken, W.: Every planar map is 4-colorable - 2: Reducibility. Ill. J. Math. 21, 491–567 (1977)

    MathSciNet  MATH  Google Scholar 

  4. Bernardini, F., Gheorghe, M.: Cell communication in tissue P systems and cell division in population P systems. Soft Comput. 9(9), 640–649 (2005)

    Article  MATH  Google Scholar 

  5. Díaz-Pernil, D., Gutierrez-Naranjo, M.A., Perez-Jimenez, M.J., Riscos-Nunez, A.: A uniform family of tissue P systems with cell division solving 3-COL in a linear time. Theoret. Comput. Sci. 404(1–2), 76–87 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Freund, R., Paun, G., Pérez-jiménez, M.J.: Tissue P systems with channel states. Theoret. Comput. Sci. 330, 101–116 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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 

  8. Linqiang, P., Pérez-Jiménez, M.J.: Computational complexity of tissue-like P systems. J. Complex. 26(3), 296–315 (2010)

    Article  MATH  Google Scholar 

  9. Gheorghe, M., Ipate, F., Lefticaru, R., Pérez-Jiménez, M.J., Turcanu, A., Valencia-Cabrera, L., Garcia-Quismondo, M., Mierla, L.: 3-Col problem modelling using simple kernel P systems. Int. J. Comput. Math. 90(4), 816–830 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Krishna, S.N., Lakshmanan, K., Rama, R.: Tissue P systems with contextual and rewriting rules. In: Păun, G., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC-CdeA 2002, LNCS, vol. 2597, pp. 339–351. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Song, B., Pan, L., Pérez-Jiménez, M.J.: Tissue P systems with protein on cells. Fundamenta Informaticae XXI, 1001–1030 (2001)

    Google Scholar 

  12. Song, B., Song, T., Pan, L.: Time-free solution to SAT problem by P systems with active membranes and standard cell division rules. Natural Computing (2014). doi: 10.1007/s11047-014-9471-4

  13. Song, B., Pan, L.: Computational efficiency and universality of timed P systems with active membranes. Theoret. Comput. Sci. 567, 74–86 (2015)

    Article  MathSciNet  Google Scholar 

  14. Martín-Vide, C., Pazos, J., Păun, G., Rodríguez-Patón, A.: Tissue P systems. Theoret. Comput. Sci. 296(2), 295–326 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Martín-Vide, C., Pazos, J., Păun, G., Rodríguez-Patón, A.: A new class of symbolic abstract neural nets: tissue P systems. In: Ibarra, O.H., Zhang, L. (eds.) COCOON 2002. LNCS, vol. 2387, p. 290. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  16. Păun, G.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Păun, G.: Membrane Computing: An Introduction. Springer-Verlag, Berlin (2002)

    Book  Google Scholar 

  18. Păun, G., Pérez-Jiménez, M.J., Riscos-Nunez, A.: Tissue P system with cell division. Int. J. Comput. Commun. Control 3(3), 295–303 (2008)

    Google Scholar 

  19. Păun, G., Rozenberg, G., Salomaa, A. (eds.): Handbook of Membrane Computing. Oxford University Press, Cambridge (2009)

    Google Scholar 

  20. Pérez-Jiménez, M.J., Romero-Jiménez, A., Sancho-Caparrini, F.: A polynomial complexity class in P systems using membrane division. J. Automata Lang. Comb. 11(4), 423–434 (2006)

    MATH  Google Scholar 

  21. Stockmeyer, L.J.: Planar 3-colorability is NP-complete. SIGACT News 5(3), 19–25 (1973)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karunya University, Coimbatore, Tamilnadu, India

    T. Mathu & Hepzibah A. Christinal

  2. Research Group on Computational Topology and Applied Mathematics, University of Sevilla, Avda. Reina Mercedes s/n, 41012, Sevilla, Spain

    Daniel Díaz-Pernil

Authors
  1. T. Mathu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hepzibah A. Christinal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Daniel Díaz-Pernil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hepzibah A. Christinal .

Editor information

Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Auckland, Auckland, New Zealand

    Michael J. Dinneen

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Mathu, T., Christinal, H.A., Díaz-Pernil, D. (2015). A Uniform Family of Tissue P Systems with Protein on Cells Solving 3-Coloring in Linear Time. In: Calude, C., Dinneen, M. (eds) Unconventional Computation and Natural Computation. UCNC 2015. Lecture Notes in Computer Science(), vol 9252. Springer, Cham. https://doi.org/10.1007/978-3-319-21819-9_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21819-9_18

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21818-2

  • Online ISBN: 978-3-319-21819-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation