Advertisement

Natural Computing

, Volume 10, Issue 1, pp 167–182 | Cite as

P systems with active membranes: trading time for space

  • Antonio E. Porreca
  • Alberto Leporati
  • Giancarlo Mauri
  • Claudio Zandron
Article

Abstract

We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = SPACE.

Keywords

Membrane computing Computational complexity Register machines 

Notes

Acknowledgements

We would like to thank Damien Woods for the suggestion to avoid object evolution rules in our solution to Q3SAT. This work was partially supported by the Italian project FIAR 2007 “Modelli di calcolo naturale e applicazioni alla Systems Biology”.

References

  1. Alhazov A, Freund R (2005) On the efficiency of P systems with active membranes and two polarizations. In: Membrane computing, fifth international workshop, WMC 2004, lecture notes in computer science, vol 3365, pp 81–94Google Scholar
  2. Ciobanu G, Marcus S, Păun G (2009) New strategies of using the rules of a P system in a maximal way: power and complexity. Romanian J Inf Sci Technol 12(2):157–173Google Scholar
  3. Freund R, Oswald M (2002) GP systems with forbidding context. Fundam Inf 49(1–3):81–102MathSciNetzbMATHGoogle Scholar
  4. Freund R, Păun G (2001) On the number of non-terminals in graph-controlled, programmed, and matrix grammars. In: Machines, computation and universality, MCU, lecture notes in computer science, vol 2055, pp 214–225Google Scholar
  5. Freund R, Păun G (2004) From regulated rewriting to computing with membranes: collapsing hierarchies. Theor Comput Sci 312:143–188zbMATHCrossRefGoogle Scholar
  6. Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman, New YorkzbMATHGoogle Scholar
  7. Gutiérrez-Naranjo MA, Pérez-Jiménez MJ, Riscos-Núñez A, Romero-Campero FJ (2006a) On the power of dissolution in P systems with active membranes. In: Membrane computing, sixth international workshop, WMC 2005, lecture notes in computer science, vol 3850, pp 224–240Google Scholar
  8. Gutiérrez-Naranjo MA, Pérez-Jiménez MJ, Riscos-Núñez A, Romero-Campero FJ, Romero-Jiménez A (2006b) Characterizing tractability by cell-like membrane systems. In: Formal models, languages and applications, series in machine perception and artificial intelligence, vol 66, pp 137–154Google Scholar
  9. Krishna SN, Rama R (1999) A variant of P systems with active membranes: solving NP-complete problems. Romanian J Inf Sci Technol 2(4):357–367Google Scholar
  10. Minsky ML (1967) Computation: finite and infinite machines. Prentice Hall, New JerseyzbMATHGoogle Scholar
  11. Obtułowicz A (2001) Deterministic P systems for solving SAT problem. Romanian J Inf Sci Technol 4(1–2):551–558Google Scholar
  12. Păun G (2000) Computing with membranes. J Comput Syst Sci 1(61):108–143CrossRefGoogle Scholar
  13. Păun G (2001) P systems with active membranes: attacking NP-complete problems. J Autom Lang Combin 6(1):75–90MathSciNetzbMATHGoogle Scholar
  14. Păun G (2002) Membrane computing: An introduction. Springer-Verlag, New YorkzbMATHGoogle Scholar
  15. Pérez-Jiménez MJ, Romero-Jiménez A, Sancho-Caparrini F (2004) The P versus NP problem through cellular computing with membranes. In: Aspects of molecular computing, lecture notes in computer science, vol 2950, pp 338–352Google Scholar
  16. Pérez-Jiménez MJ, Romero-Jiménez A, Sancho-Caparrini F (2006) A polynomial complexity class in P systems using membrane division. J Autom Lang Combin 11(4):423–434. A preliminary version appears in: Proceedings of the fifth international workshop on descriptional complexity of formal systems, 2003, pp 284–294Google Scholar
  17. Porreca AE, Leporati A, Mauri G, Zandron C (2009) Introducing a space complexity measure for P systems. Int J Comput Commun Control 4(3):301–310Google Scholar
  18. Sosik P (2003) The computational power of cell division: beating down parallel computers? Nat Comput 2(3):287–298MathSciNetzbMATHCrossRefGoogle Scholar
  19. The P Systems Webpage (2000). http://www.ppage.psystems.eu
  20. Zandron C, Ferretti C, Mauri G (2000) Solving NP-complete problems using P systems with active membranes. In: Antoniou CS, Calude MJ, Dinneen I (eds) Unconventional models of computation. Springer-Verlag, London, pp 289–301Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

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

Personalised recommendations