Skip to main content
SpringerLink
Log in

Computing with Membranes: Attacking NP-Complete Problems

  • Conference paper
Unconventional Models of Computation, UMC’2K

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

The aim of this paper is to introduce to the reader the main ideas of Computing with Membranes, a recent branch of (theoretical) Molecular Computing, with emphasis on some variants which can solve computationally hard problems in polynomial (often, linear) time. In short, in a cell-like system (called a P system), multisets of objects (described by symbols or by strings of symbols) evolve in a membrane structure and compute natural numbers as the result of halting sequences of transitions. The model is parallel, distributed, and non-deterministic.

We present here informally the model, we illustrate by an example the basic definition, then we recall several variants which can solve NP-complete problems in a polynomial time. A complete bibliography of the domain, at the level of the end of August 2000, is also provided.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

Bibliography of P systems (August 2000)

  1. A. Atanasiu, Arithmetic with membranes, Pre-proc. of Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

  2. A. V. Baranda, J. Castellanos, F. Arroyo, R. Gonzalo, Data structures for implementing P systems in silico, Pre-proc. of Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

  3. C. Calude, Gh. Păun, Computing with Cells and Atoms, Taylor and Francis, London, 2000 (Chapter 3: “Computing with Membranes”).

    Google Scholar 

  4. J. Castellanos, Gh. Păun, A. Rodriguez-Paton, Computing with membranes: P systems with worm-objects, IEEE Conf. SPIRE 2000, La Coruna, Spain, and Auckland University, CDMTCS Report No 123,2000 (www.cs.auckland.ac.nz/CDMTCS).

    Google Scholar 

  5. J. Dassow, Gh. Păun, On the power of membrane computing, J. of Universal Computer Sci., 5, 2 (1999),33–49 (www.iicm.edu/jucs)

    Google Scholar 

  6. J. Dassow, Gh. Păun, Concentration controlled P systems, submitted, 1999.

    Google Scholar 

  7. R. Freund, Generalized P systems, Fundamentals of Computation Theory, FCT’99, Iaşi, 1999 (G. Ciobanu, Gh. Păun, eds.), LNCS 1684, Springer, 1999, 281–292.

    Google Scholar 

  8. R. Freund, Generalized P systems with splicing and cutting/recombination, Workshop on Formal Languages, FCT99, Iaşi, 1999.

    Google Scholar 

  9. R. Freund, F. Freund, Molecular computing with generalized homogeneous P systems, Proc. Conf. DNA6 (A. Condon, G. Rozenberg, eds.), Leiden, 2000, 113–125.

    Google Scholar 

  10. P. Frisco, Membrane computing based on splicing: improvements, Pre-proc. of Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

  11. M. Ito, C. Martin-Vide, Gh. Păun, A characterization of Parikh sets of ETOL languages in terms of P systems, submitted, 2000.

    Google Scholar 

  12. S. N. Krishna, Computing with simple P systems, Pre-proc. Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

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

    Google Scholar 

  14. S. N. Krishna, R. Rama, On the power of P systems with sequential and parallel rewriting, Intern. J. Computer Math., 77,1-2 (2000), 1–14.

    Google Scholar 

  15. S. N. Krishna, R. Rama, Computing with P systems, submitted, 2000.

    Google Scholar 

  16. S. N. Krishna, R. Rama, On simple P systems with external output, submitted, 2000.

    Google Scholar 

  17. M. Malita, Membrane computing in Prolog, Pre-proc. of Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

  18. C. Martin-Vide, V. Mitrana, P systems with valuations, submitted, 2000.

    Google Scholar 

  19. C. Martin-Vide, Gh. Păun, Computing with membranes. One more collapsing hierarchy, Bulletin of the EATCS, to appear.

    Google Scholar 

  20. C. Martin-Vide, Gh. Păun, String objects in P systems, Proc. of Algebraic Systems, Formal Languages and Computations Workshop, Kyoto, 2000, RIMS Kokyuroku Series, Kyoto Univ., 2000.

    Google Scholar 

  21. C. Martin-Vide, Gh. Păun, G. Rozenberg, Plasmid-based P systems, submitted, 2000.

    Google Scholar 

  22. A. Păun, On P systems with membrane division, submitted, 2000.

    Google Scholar 

  23. A. Păun, M. Păun, On the membrane computing based on splicing, submitted, 2000.

    Google Scholar 

  24. Gh. Păun, Computing with membranes, Journal of Computer and System Sciences, 61 (2000), in press, and Turku Center for Computer Science-TUCS Report No 208, 1998 (www.tucs.fi).

  25. Gh. Păun, Computing with membranes. An introduction, Bulletin of the EATCS, 67 (Febr. 1999), 139–152.

    MATH  Google Scholar 

  26. Gh. Păun, Computing with membranes-A variant: P systems with polarized membranes, Intern. J. of Foundations of Computer Science, 11, 1 (2000),167–182.

    Article  Google Scholar 

  27. Gh. Păun, P systems with active membranes: Attacking NP complete problems, J. Automata, Languages, and Combinatorics, 5 (2000), in press, and Auckland University, CDMTCS Report No 102,1999 (www.cs.auckland.ac.nz/CDMTCS).

    Google Scholar 

  28. Computing with membranes (P systems): Twenty six research topics, Auckland University, CDMTCS Report No 119,2000 (www.cs.auckland.ac.nz/CDMTCS).

    Google Scholar 

  29. Gh. Păun, G. Rozenberg, A. Salomaa, Membrane computing with external output, Fundamenta Informaticae, 41, 3 (2000),259–266.

    MathSciNet  Google Scholar 

  30. Gh. Păun, Y. Sakakibara, T. Yokomori, P systems on graphs of restricted forms, submitted, 1999.

    Google Scholar 

  31. Gh. Păun, Y. Suzuki, H. Tanaka, P Systems with energy accounting, submitted, 2000.

    Google Scholar 

  32. Gh. Păun, Y. Suzuki, H. Tanaka, T. Yokomori, On the power of membrane division in P systems, Proc. Words, Semigroups, Combinatorics Conf., Kyoto, 2000.

    Google Scholar 

  33. Gh. Păun, G. Thierrin, Multiset processing by means of systems of finite state transducers, Pre-Proc. of Workshop on Implementing Automata WIA99, Potsdam, August 1999, Preprint 5/1999 ofUniv. Potsdam (O. Boldt, H. Jürgensen, L. Robbins, eds.) XV 1–17.

    Google Scholar 

  34. Gh. Păun, T. Yokomori, Membrane computing based on splicing, Preliminary Proc. of Fifth Intern. Meeting on DNA Based Computers (E. Winfree, D. Gifford, eds.), MIT, June 1999,213–227.

    Google Scholar 

  35. Gh. Păun, T. Yokomori, Simulating H systems by P systems, Journal of Universal Computer Science, 6, 2 (2000), 178–193 (www.iicm.edu/jucs).

    MATH  Google Scholar 

  36. Gh. Păun, S. Yu, On synchronization in P systems, Fundamenta Informaticae, 38, 4 (1999),397–410.

    MathSciNet  MATH  Google Scholar 

  37. I. Petre, A normal form for P systems, Bulletin of the EATCS, 67 (Febr. 1999), 165–172.

    MathSciNet  MATH  Google Scholar 

  38. I. Petre, L. Petre, Mobile ambients and P systems, J. Universal Computer Sci., 5, 9 (1999),588–598.

    MathSciNet  MATH  Google Scholar 

  39. Y. Suzuki, H. Tanaka, On a USP implementation of a class of P systems, Romanian J. of Information Science and Technology, 3, 2 (2000).

    Google Scholar 

  40. Y. Suzuki, H. Tanaka, Artificial life and P systems, Pre-proc. Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

  41. Cl. Zandron, Cl. Ferretti, G. Mauri, Two normal forms for rewriting P systems, submitted, 2000.

    Google Scholar 

  42. Cl. Zandron, Cl. Ferretti, G. Mauri, Priorities and variable thickness of membranes in rewriting P systems, submitted, 2000.

    Google Scholar 

  43. Cl. Zandron, Cl. Ferretti, G. Mauri, Solving NP-complete problems using P systems with active membranes, submitted, 2000.

    Google Scholar 

  44. Cl. Zandron, Cl. Ferretti, G. Mauri, Using membrane features in P systems, Preproc. of Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000.

    Google Scholar 

References

  1. L. M. Adleman, Molecular computation of solutions to combinatorial problems, Science, 226 (November 1994),1021–1024.

    Article  Google Scholar 

  2. G. Berry, G. Boudol, The chemical abstract machine, Theoretical Computer Sci., 96 (1992),217–248.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. Bray, Protein molecules as computational elements in living cells, Nature, 376 (1995),307–312

    Article  Google Scholar 

  4. M. R. Garey, D. J. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, W. H. Freeman and Comp., San Francisco, 1979.

    Google Scholar 

  5. T. Head, Formal language theory and DNA: An analysis of the generative capacity of specific recombinant behaviors, Bulletin of Mathematical Biology, 49 (1987), 737–759.

    MathSciNet  MATH  Google Scholar 

  6. R. J. Lipton, Using DNA to solve NP-complete problems, Science, 268 (April 1995), 542–545.

    Article  Google Scholar 

  7. W. R. Loewenstein, The Touchstone of Life. Molecular Information, Cell Communication, and the Foundations of Life, Oxford Univ. Press, New York, Oxford, 1999.

    Google Scholar 

  8. Gh. Păun, G. Rozenberg, A. Salomaa, DNA Computing. New Computing Paradigms, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  9. G. Rozenberg, A. Salomaa, eds., Handbook of Formal Languages, 3 volumes, Springer-Verlag, Berlin, 1997.

    MATH  Google Scholar 

  10. M. Sipper, Studying Artificial Life using a simple, general cellular model, Artificial Life Journal, 2, 1 (1995), 1–35.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy, Bucureşti, Romania

    Gheorghe Păun

Authors
  1. Gheorghe Păun
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Solvay Institutes, Free University of Brussels, Belgium

    I. Antoniou

  2. Department of Computer Science, University of Auckland, Auckland, New Zealand

    C. S. Calude  & M. J. Dinneen  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London

About this paper

Cite this paper

Păun, G. (2001). Computing with Membranes: Attacking NP-Complete Problems. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0313-4_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-415-4

  • Online ISBN: 978-1-4471-0313-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation