Natural Computing

, Volume 11, Issue 2, pp 253–259 | Cite as

Membrane system models for super-Turing paradigms

  • Marian GheorgheEmail author
  • Mike Stannett


We extend Calude and Păun’s accelerating P system model of computation, and investigate the computational power of the resulting systems. We show that the resulting systems can solve problems at all levels of the arithmetical hierarchy, and that the higher systems have hyperarithmetical computational power.


P system Membrane system Hypercomputation Super-Turing Arithmetical hierarchy Hyperarithmetical hierarchy 



A preliminary version of this material was presented at the UC09 Hypercomputation Workshop, Ponta Delgada, The Azores, 7–11 September 2009. The authors would like to thank the anonymous reviewers for their helpful comments. This research was funded in part by the EPSRC (HyperNet, Grant Ref. EP/E064183/1). MG’s research is also partially funded by CNCSIS grant no. 643/2009.


  1. Alberts B, Johnson A, Walter P, Lewis J, Raff M, Roberts K (2008) Molecular biology of the cell, 5th edn. Garland Publishing Inc., New YorkGoogle Scholar
  2. Ash CJ, Knight JF (2000) Computable structures and the hyperarithmetical hierarchy. Elsevier, AmsterdamzbMATHGoogle Scholar
  3. Bernardini F, Gheorghe M (2004) Population P systems. J Univers Comput Sci 10:509–539MathSciNetGoogle Scholar
  4. Calude CS, Păun G (2004) Bio-steps beyond Turing. BioSystems 77:175–194CrossRefGoogle Scholar
  5. Calude CS, Staiger L (2010) A note on accelerated Turing machines. Math Struct Comput Sci 20:1011–1017MathSciNetzbMATHCrossRefGoogle Scholar
  6. Câmpeanu C, Păun A (2005) Computing beyond Turing limit using H systems. In: Ferretti C, Mauri G, Zandron C (eds) 10th international workshop on DNA Computing, DNA10, Milan, Italy, June 7–10, 2004, Revised Selected Papers. number 3384 in Lecture notes in computer science, pp 24–34. Springer, BerlinGoogle Scholar
  7. Cavaliere M, Leupold P (2006) Observation of string-rewriting systems. Fundam Inf 74:447–462MathSciNetzbMATHGoogle Scholar
  8. Chatelin F (2010) A computational journey into nonlinearity. In: Calude CS, Hagiya M, Morita K, Rozenberg G, Timmis J (eds) Unconventional computation—9th international conference, UC 2010, Tokyo, Japan, June 21–25, 2010. Proceedings, number 6079 in Lecture notes in computer science, pp 3–5. Springer, BerlinGoogle Scholar
  9. Etesi G, Németi I (2002) Non-Turing computations via Malament-Hogarth space-times. Int J Theor Phys 41:341–370. arXiv:gr-qc/0104023v2Google Scholar
  10. Gillessen S et al (2009). Monitoring stellar orbits around the massive black hole in the Galactic Center. Astrophys J 692:1075–1109. doi: 10.1088/0004-637X/692/2/1075 Google Scholar
  11. Hogarth M (2004) Deciding arithmetic using SAD computers. Br J Philos Sci 55:681–691MathSciNetzbMATHCrossRefGoogle Scholar
  12. O’Neill B (1995) The geometry of Kerr black holes. A K Peters, WellesleyzbMATHGoogle Scholar
  13. Păun G (2000) Computing with membranes. J Comput Syst Sci 61:108–143zbMATHCrossRefGoogle Scholar
  14. Păun, G, Rozenberg, G, Salomaa, A (eds) (2010) The Oxford handbook of membrane computing. Oxford University Press, OxfordzbMATHGoogle Scholar
  15. Rogers H (1967) The theory of recursive functions and effective computability. MIT Press, CambridgeGoogle Scholar
  16. Sosik P, Valik O (2006) On evolutionary lineages of membrane systems. In: Freund R, Păun G, Rozenberg G, Salomaa A (eds) 6th international workshop, WMC 2005, Vienna, Austria, July 18–21, 2005. Revised Selected and Invited Papers, number 3850 in Lecture notes in computer science, pp 67–78. Springer, BerlinGoogle Scholar
  17. Syropoulos A (2006) Fuzzifying P systems. Comput J. 49:619–628CrossRefGoogle Scholar
  18. Turing AM (1936) On computable numbers, with an application to the Entscheidungsproblem. Proc Lond Math Soc (2) 42:230–265. doi: 10.1112/plms/s2-42.1.230 (With subsequent correction 43:544–546)

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Sheffield Regent CourtSheffieldUK
  2. 2.Department of Computer ScienceUniversity of PitestiPitestiRomania

Personalised recommendations