Skip to main content
SpringerLink
Log in

Universality of spiking neural P systems with polarizations working in sequential mode induced by maximum spike number

  • Regular Paper
  • Published:
Journal of Membrane Computing Aims and scope Submit manuscript

Abstract

Based on the inspiration that the communication signal between neurons in biology is composed of short electrical pulses, we investigate a new variant of spiking neural P systems, i.e., spiking neural P systems with polarizations (PSN P systems), which have a rule-triggering condition associated with polarization. In this work, we focus on the computational power of sequential PSN P systems with delay based on the maximum number of spikes, i.e., the ability to preferentially fire the neuron with the maximum number of spikes among the active neurons at each step (except for the neurons in the refractory period) of the computation. Thus, two strategies are considered, i.e., the max-sequentiality strategy and the max-pseudo-sequentiality strategy, and we prove that PSN P systems with delay adopting the max-sequentiality strategy or the max-pseudo-sequentiality strategy are Turing universal as number generating devices. The results give positive answers to the open problem formulated in [Tingfang Wu et al. (2020), Neurocomputing, 401, 392–404].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Chen, H., Freund, R., Ionescu, M., Păun, G., & Pérez-Jiménez, M. J. (2007). On string languages generated by spiking neural P systems. Fundamenta Informaticae, 75(1–4), 141–162.

    MathSciNet  MATH  Google Scholar 

  2. Chen, Z., Zhang, P., Wang, X., Shi, X., Wu, T., & Zheng, P. (2018). A computational approach for nuclear export signals identification using spiking neural P systems. Neural Computing and Applications, 29(3), 695–705.

    Article  Google Scholar 

  3. Diaz, C., Frias, T., Sanchez, G., Perez, H., Toscano, K., & Duchen, G. (2017). A novel parallel multiplier using spiking neural P systems with dendritic delays. Neurocomputing, 239, 113–121.

    Article  Google Scholar 

  4. Díaz-Pernil, D., Peña-Cantillana, F., & Gutiérrez-Naranjo, M. A. (2013). A parallel algorithm for skeletonizing images by using spiking neural P systems. Neurocomputing, 115, 81–91.

    Article  Google Scholar 

  5. Fan, S., Paul, P., Wu, T., Rong, H., & Zhang, G. (2020). On applications of spiking neural P systems. Applied Sciences, 10(20), 7011.

    Article  Google Scholar 

  6. Garcia, L., Sanchez, G., Vazquez, E., Avalos, G., Anides, E., Nakano, M., Sanchez, G., & Perez, H. (2021). Small universal spiking neural P systems with dendritic/axonal delays and dendritic trunk/feedback. Neural Networks, 138, 126–139.

    Article  Google Scholar 

  7. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Single neurons, populations, plasticity. Cambridge University Press.

    Book  MATH  Google Scholar 

  8. Gutiérrez-Naranjo, M. A., & Leporati, A. (2009). First steps towards a cpu made of spiking neural P systems. International Journal of Computers Communications & Control, 4(3), 244–252.

    Article  Google Scholar 

  9. Hertz, J., Krogh, A., & Palmer, R. G. (2018). Introduction to the theory of neural computation. CRC Press.

    Book  Google Scholar 

  10. Ibarra, O. H., Păun, A., & Rodríguez-Patón, A. (2009). Sequential SNP systems based on min/max spike number. Theoretical Computer Science, 410, 2982–2991.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ionescu, M., Păun, G., & Yokomori, T. (2006). Spiking neural P systems. Fundamenta Informaticae, 71(2—-3), 279–308.

    MathSciNet  MATH  Google Scholar 

  12. Ishdorj, T. O., Leporati, A., Pan, L., Zeng, X., & Zhang, X. (2010). Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources. Theoretical Computer Science, 411(25), 2345–2358.

    Article  MathSciNet  MATH  Google Scholar 

  13. Jiang, S., Fan, J., Liu, Y., Wang, Y., & Xu, F. (2020). Spiking neural P systems with polarizations and rules on synapses. Complexity, 2020(1), 12.

    MATH  Google Scholar 

  14. Jiang, Y., Su, Y., & Luo, F. (2019). An improved universal spiking neural P system with generalized use of rules. Journal of Membrane Computing, 1(4), 270–278.

    Article  MathSciNet  MATH  Google Scholar 

  15. Krithivasan, K., Metta, V. P., & Garg, D. (2011). On string languages generated by spiking neural P systems with anti-spikes. International Journal of Foundations of Computer Science, 22(1), 15–27.

    Article  MathSciNet  MATH  Google Scholar 

  16. Leporati, A., Mauri, G., Zandron, C., Păun, G., & Pérez-Jiménez, M. J. (2009). Uniform solutions to SAT and Subset Sum by spiking neural P systems. Natural Computing, 8(4), 681–702.

    Article  MathSciNet  MATH  Google Scholar 

  17. Li, J., Huang, Y., & Xu, J. (2016). Decoder design based on spiking neural P systems. IEEE Transactions on Nanobioscience, 15(7), 639–644.

    Article  Google Scholar 

  18. Maass, W. (1997). Networks of spiking neurons: the third generation of neural network models. Neural Networks, 10(9), 1659–1671.

    Article  Google Scholar 

  19. Maass, W. (1997). The Third generation of neural network models. Technische Universitat Gräz.

    Google Scholar 

  20. Maass, W., & Bishop, C. M. (2001). Pulsed neural networks. MIT Press.

    MATH  Google Scholar 

  21. Neary, T. (2015). Three small universal spiking neural P systems. Theoretical Computer Science, 567, 2–20.

    Article  MathSciNet  MATH  Google Scholar 

  22. Pan, L., Păun, G., Zhang, G., & Neri, F. (2017). Spiking neural P systems with communication on request. International Journal of Neural Systems, 27(08), 1750042.

    Article  Google Scholar 

  23. Pan, L., Wu, T., Su, Y., & Vasilakos, A. V. (2017). Cell-like spiking neural P systems with request rules. IEEE Transactions on NanoBioscience, 16(6), 513–522.

    Article  Google Scholar 

  24. Pan, L., & Zeng, X. (2011). Small universal spiking neural P systems working in exhaustive mode. IEEE Transactions on NanoBioscience, 10(2), 99–105.

    Article  Google Scholar 

  25. Pan, T., Shi, X., Zhang, Z., & Xu, F. (2018). A small universal spiking neural P system with communication on request. Neurocomputing, 275, 1622–1628.

    Article  Google Scholar 

  26. Păun, A., & Păun, G. (2007). Small universal spiking neural P systems. BioSystems, 90(1), 48–60.

    Article  MATH  Google Scholar 

  27. Păun, G. (2000). Computing with membranes. Journal of Computer and System Sciences, 61(1), 108–143.

    Article  MathSciNet  MATH  Google Scholar 

  28. Păun, G. (2002). Membrane computing: An introduction. Springer-Verlag.

    Book  MATH  Google Scholar 

  29. Păun, G. (2010). A quick introduction to membrane computing. The Journal of Logic and Algebraic Programming, 79(6), 291–294.

    Article  MathSciNet  MATH  Google Scholar 

  30. Păun, G., Rozenberg, G., & Salomaa, A. (2010). The Oxford handbook of membrane computing. Oxford University Press.

    Book  MATH  Google Scholar 

  31. Peng, H., Wang, J., Ming, J., Shi, P., Pérez-Jiménez, M. J., Yu, W., & Tao, C. (2017). Fault diagnosis of power systems using intuitionistic fuzzy spiking neural P systems. IEEE Transactions on Smart Grid, 9(5), 4777–4784.

    Article  Google Scholar 

  32. Peng, H., Wang, J., Pérez-Jiménez, M. J., Wang, H., Shao, J., & Wang, T. (2013). Fuzzy reasoning spiking neural P systems for fault diagnosis. Information Sciences, 235, 106–116.

    Article  MathSciNet  MATH  Google Scholar 

  33. Song, T., & Pan, L. (2016). Spiking neural P systems with request rules. Neurocomputing, 193, 193–200.

    Article  Google Scholar 

  34. Song, T., Pan, L., & Păun, G. (2013). Asynchronous spiking neural P systems with local synchronization. Information Sciences, 219, 197–207.

    Article  MathSciNet  MATH  Google Scholar 

  35. Song, T., Pan, L., & Păun, G. (2014). Spiking neural P systems with rules on synapses. Theoretical Computer Science, 529, 82–95.

    Article  MathSciNet  MATH  Google Scholar 

  36. Song, T., Pan, L., Wu, T., Zheng, P., Wong, M. D., & Rodríguez-Patón, A. (2019). Spiking neural P systems with learning functions. IEEE Transactions on Nanobioscience, 18(2), 176–190.

    Article  Google Scholar 

  37. Song, T., Pang, S., Hao, S., Rodríguez-Patón, A., & Zheng, P. (2019). A parallel image skeletonizing method using spiking neural P systems with weights. Neural Processing Letters, 50(2), 1485–1502.

    Article  Google Scholar 

  38. Wang, J., Peng, H., Yu, W., Ming, J., Pérez-Jiménez, M. J., Tao, C., & Huang, X. (2019). Interval-valued fuzzy spiking neural P systems for fault diagnosis of power transmission networks. Engineering Applications of Artificial Intelligence, 82, 102–109.

    Article  Google Scholar 

  39. Wang, J., Shi, P., Peng, H., Pérez-Jiménez, M. J., & Wang, T. (2013). Weighted fuzzy spiking neural P systems. IEEE Transactions on Fuzzy Systems, 21(2), 209–220.

    Article  Google Scholar 

  40. Wang, T., Zhang, G., Zhao, J., He, Z., Wang, J., & Pérez-Jiménez, M. J. (2014). Fault diagnosis of electric power systems based on fuzzy reasoning spiking neural P systems. IEEE Transactions on Power Systems, 30(3), 1182–1194.

    Article  Google Scholar 

  41. Wu, T., Bîlbîe, F. D., Păun, A., Pan, L., & Neri, F. (2018). Simplified and yet turing universal spiking neural P systems with communication on request. International Journal of Neural Systems, 28(08), 1850013.

    Article  Google Scholar 

  42. Wu, T., & Pan, L. (2020). The computation power of spiking neural P systems with polarizations adopting sequential mode induced by minimum spike number. Neurocomputing, 401, 392–404.

    Article  Google Scholar 

  43. Wu, T., Pan, L., & Alhazov, A. (2019). Computation power of asynchronous spiking neural P systems with polarizations. Theoretical Computer Science, 777, 474–489.

    Article  MathSciNet  MATH  Google Scholar 

  44. Wu, T., Păun, A., Zhang, Z., & Pan, L. (2018). Spiking neural P systems with polarizations. IEEE Transactions on Neural Networks and Learning Systems, 29(8), 3349–3360.

    Article  MathSciNet  Google Scholar 

  45. Wu, T., Zhang, T., & Xu, F. (2020). Simplified and yet turing universal spiking neural P systems with polarizations optimized by anti-spikes. Neurocomputing, 414, 255–266.

    Article  Google Scholar 

  46. Wu, T., Zhang, Z., & Pan, L. (2016). On languages generated by cell-like spiking neural P systems. IEEE Transactions on Nanobioscience, 15(5), 455–467.

    Article  Google Scholar 

  47. Wu, T., Zhang, Z., Păun, G., & Pan, L. (2016). Cell-like spiking neural P systems. Theoretical Computer Science, 623, 180–189.

    Article  MathSciNet  MATH  Google Scholar 

  48. Zeng, X., Xu, L., Liu, X., & Pan, L. (2014). On languages generated by spiking neural P systems with weights. Information Sciences, 278, 423–433.

    Article  MathSciNet  MATH  Google Scholar 

  49. Zhang, G., Pérez-Jiménez, M. J., & Gheorghe, M. (2017). Real-life applications with membrane computing. Springer.

    Book  MATH  Google Scholar 

  50. Zhang, G., Rong, H., Neri, F., & Pérez-Jiménez, M. J. (2014). An optimization spiking neural P system for approximately solving combinatorial optimization problems. International Journal of Neural Systems, 24(05), 1440006.

    Article  Google Scholar 

  51. Zhang, X., Zeng, X., & Pan, L. (2008). Smaller universal spiking neural P systems. Fundamenta Informaticae, 87(1), 117–136.

    MathSciNet  MATH  Google Scholar 

  52. Zhang, X., Zeng, X., & Pan, L. (2009). On languages generated by asynchronous spiking neural P systems. Theoretical Computer Science, 410(26), 2478–2488.

    Article  MathSciNet  MATH  Google Scholar 

  53. Zhao, Y., Liu, X., & Wang, W. (2016). Spiking neural P systems with neuron division and dissolution. Plos One, 11(9), 0162882.

    Article  Google Scholar 

  54. Zhu, M., Yang, Q., Dong, J., Zhang, G., Gou, X., Rong, H., Paul, P., & Neri, F. (2021). An adaptive optimization spiking neural P system for binary problems. International Journal of Neural Systems, 31(01), 2050054.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by Anhui Provincial Natural Science Foundation (No. 1808085MF173).

Author information

Authors and Affiliations

  1. The University Key Laboratory of Intelligent Perception and Computing of Anhui Province, Anqing Normal University, Anqing, 246133, Anhui, China

    Li Liu & Keqin Jiang

  2. School of Computer and Information, Anqing Normal University, Anqing, 246133, Anhui, China

    Li Liu & Keqin Jiang

Authors
  1. Li Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keqin Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Keqin Jiang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, L., Jiang, K. Universality of spiking neural P systems with polarizations working in sequential mode induced by maximum spike number. J Membr Comput 4, 56–67 (2022). https://doi.org/10.1007/s41965-021-00088-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41965-021-00088-w

Keywords

Search

Navigation