Natural Computing

, Volume 7, Issue 4, pp 499–517 | Cite as

Characterizations of some classes of spiking neural P systems



We look at the recently introduced neural-like systems, called SN P systems. These systems incorporate the ideas of spiking neurons into membrane computing. We study various classes and characterize their computing power and complexity. In particular, we analyze asynchronous and sequential SN P systems and present some conditions under which they become (non-)universal. The non-universal variants are characterized by monotonic counter machines and partially blind counter machines and, hence, have many decidable properties. We also investigate the language-generating capability of SN P systems.


Spiking neural P system Asynchronous mode Sequential mode Partially blind counter machine Semilinear set Language generator 



This research was supported in part by NSF Grants CCF-0430945 and CCF-0524136.


  1. Cavaliere M, Egecioglu O, Ibarra OH, Ionescu M, Păun Gh, Woodworth S (2007) Asynchronous spiking neural P systems; decidability and undecidability. Proceedings of DNA13, LNCS 4848. SpringerGoogle Scholar
  2. Chen H, Ionescu M, Păun A, Păun Gh, Popa B (2006) On trace languages generated by (small) spiking neural P systems. Pre-proc 8th workshop on descriptional complexity of formal systems, June 2006Google Scholar
  3. Chen H, Freund R, Ionescu M, Păun Gh, Pérez-Jiménez MJ (2007) On string languages generated by spiking neural P systems. Fundam Informaticae 75(1–4):141–162MATHGoogle Scholar
  4. Chen H, Ionescu M, Ishdorj T-O, Păun A, Păun Gh, Pérez-Jiménez MJ (2008) Spiking neural P systems with extended rules: Universality and languages. Nat Comput (special issue devoted to DNA12 Conf). doi: 10.1007/s11047-006-9024-6
  5. Gerstner W, Kistler W (2002) Spiking neuron models. Single neurons, populations, plasticity. Cambridge University PressGoogle Scholar
  6. Greibach S (1978) Remarks on blind and partially blind one-way multicounter machines. Theor Comput Sci 7(3):311–324MATHCrossRefMathSciNetGoogle Scholar
  7. Harju T, Ibarra O, Karhumaki J, Salomaa A (2002) Some decision problems concerning semilinearity and commutation. J Comput Syst Sci 65:278–294MATHCrossRefMathSciNetGoogle Scholar
  8. Ibarra OH, Woodworth S (2006) Characterizations of some restricted spiking neural P systems. Proceedings of 7th workshop on membrane computing. LNCS 4361:424–442Google Scholar
  9. Ibarra OH, Woodworth S (2007a) Characterizing regular languages by spiking neural P systems. Int J Found Comput Sci 18(6):1247–1256CrossRefMathSciNetGoogle Scholar
  10. Ibarra OH, Woodworth S (2007b) Spiking neural P systems: some characterizations. Proceedings of 16th international symposium on fundamentals of computation theory. Springer LNCS 4639:23–37Google Scholar
  11. Ibarra OH, Woodworth S, Yu F, Păun A (2006) On spiking neural P systems and partially blind counter machines. Proceedings of 5th international conference on unconventional computation, LNCS 4135, Springer, Berlin, pp 113–129Google Scholar
  12. Ibarra OH, Păun A, Păun Gh, Rodríguez-Patón A, Sosik P, Woodworth S (2007) Normal forms for spiking neural P systems. Theor Comput Sci 372(2–3):196–217MATHCrossRefGoogle Scholar
  13. Ionescu M, Păun Gh, Yokomori T (2006) Spiking neural P systems. Fundam Informaticae 71(2–3):279–308MATHGoogle Scholar
  14. Maass W (2002) Computing with spikes. Special Issue on Foundations of Information Processing of TELEMATIK 8(1):32–36Google Scholar
  15. Maass W, Bishop C (eds) (1999) Pulsed neural networks. MIT Press, CambridgeGoogle Scholar
  16. Păun Gh (2002) Membrane computing—an introduction. Springer, BerlinMATHGoogle Scholar
  17. Păun A, Păun Gh (2007) Small universal spiking neural P systems. BioSystems 90(1):48–60CrossRefGoogle Scholar
  18. Păun Gh, Pérez-Jiménez MJ, Rozenberg G (2006) Spike trains in spiking neural P systems. Int J Found Comput Sci 17(4):975–1002MATHCrossRefGoogle Scholar
  19. The P Systems Web Page (2008). Accessed on 21 October 2004

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA

Personalised recommendations