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Computational power of sequential spiking neural P systems with multiple channels

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Abstract

Spiking neural P systems with multiple channels (SNP-MC systems, for short) are a kind of distributed parallel computing devices, inspired by the way that neurons communicate by means of spikes as well as one or more synaptic channels. SNP-MC systems working in synchronous mode have been investigated. This paper discusses SNP-MC systems working in sequential mode, i.e., sequential SNP-MC systems (SSNP-MC systems, for short). The combination of two sequential sub-modes and two strategies of rule application is considered, that is, four sequentiality strategies. It is proven that SSNP-MC systems working in four sequentiality strategies are Turing universal number generating and accepting devices, respectively.

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References

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

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Păun, G., Rozenberg, G., & Salomaa, A. (2010). The Oxford handbook of membrane computing. New York: Oxford University Press.

    Book  MATH  Google Scholar 

  4. Păun, G. (2007). Spiking neural P systems with astrocyte-like control. Journal of Universal Computer Science, 13(11), 1707–1721.

    MathSciNet  Google Scholar 

  5. Pan, L., Wang, J., & Hoogeboom, H. J. (2012). Spiking neural P systems with astrocytes. Neural Computation, 24(3), 805–825.

    Article  MathSciNet  MATH  Google Scholar 

  6. Pan, L., & Păun, G. (2009). Spiking neural P systems with anti-spikes. International Journal of Computers Communications & Control, 4(3), 273–282.

    Article  Google Scholar 

  7. 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 

  8. Song, T., & Pan, L. (2015). Spiking neural P systems with rules on synapses working in maximum spiking strategy. IEEE Transactions on Nanobioscience, 14(4), 465–477.

    Article  Google Scholar 

  9. Peng, H., Chen, R., Wang, J., Song, X., Wang, T., Yang, F., & Sun, Z. (2017). Competitive spiking neural P systems with rules on synapses. IEEE Transactions on NanoBioscience, 16(8), 888–895.

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Cabarle, F. G. C., Adorna, H. N., Pérez-Jiménez, M. J., & Song, T. (2015). Spiking neural P systems with structural plasticity. Neural Computing and Applications, 26(8), 1905–1917.

    Article  MATH  Google Scholar 

  12. Wu, T., Păun, A., Zhang, Z., & Pan, L. (2017). Spiking neural P systems with polarizations. IEEE Transactions on Neural Networks and Learning Systems, 29(8), 3349–3360.

    MathSciNet  Google Scholar 

  13. 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 

  14. Peng, H., & Wang, J. (2018). Coupled neural P systems. IEEE Transactions on Neural Networks and Learning Systems, 30(6), 1672–1682.

    Article  MathSciNet  Google Scholar 

  15. Peng, H., Wang, J., Pérez-Jiménez, M. J., & Riscos-Núñez, A. (2019). Dynamic threshold neural P systems. Knowledge-Based Systems, 163, 875–884.

    Article  Google Scholar 

  16. Peng, H., Li, B., Wang, J., Song, X., Wang, T., Valencia-Cabrera, L., Pérez-Hurtado, I., Riscos-Núñez, A., & Pérez-Jiménez, M. J. (2020a). Spiking neural P systems with inhibitory rules. Knowledge-Based Systems, 188, 105064.

    Article  Google Scholar 

  17. Peng, H., Bao, T., Luo, X., Wang, J., Song, X., Riscos-Núñez, A., & Pérez-Jiménez, MJ. (2020). Dendrite P systems. Neural Networks 127:110–120

  18. Peng, H., Lv, Z., Li, B., Luo, X., Wang, J., Song, X., et al. (2020). Nonlinear spiking neural P systems. International Journal of Neural Systems, 30(10), 2050008 (1-17).

    Article  Google Scholar 

  19. Cabarle, F., Zeng, X., Murphy, N., Song, T., Rodríguez-Patón, A., & Liu, X. (2021). Neural-like P systems with plasmids. Information and Computation, 1, 104766.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. Wang, J., Shi, P., Peng, H., Pérez-Jiménez, M. J., & Wang, T. (2012). Weighted fuzzy spiking neural P systems. IEEE Transactions on Fuzzy Systems, 21(2), 209–220.

    Article  Google Scholar 

  22. Wu, T., & Jiang, S. (2021). Spiking neural P systems with a flat maximally parallel use of rules. Journal of Membrane Computing, 3, 221–231.

    Article  MathSciNet  Google Scholar 

  23. Cruz, R., Cabarle, F., & Adorna, H. (2019). Generating context-free languages using spiking neural P systems with structural plasticity. Journal of Membrane Computing, 1, 161–177.

    Article  MathSciNet  MATH  Google Scholar 

  24. 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 

  25. 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 

  26. Peng, H., Wang, J., Shi, P., Pérez-Jiménez, M. J., & Riscos-Núñez, A. (2017a). Fault diagnosis of power systems using fuzzy tissue-like P systems. Integrated Computer-Aided Engineering, 24(4), 401–411.

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. 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 

  29. 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 

  30. Díaz-Pernil, D., Gutiérrez-Naranjo, M. A., & Peng, H. (2019). Membrane computing and image processing: A short survey. Journal of Membrane Computing, 1(1), 58–73.

    Article  MathSciNet  Google Scholar 

  31. Li, B., Peng, H., Wang, J., & Huang, X. (2020). Multi-focus image fusion based on dynamic threshold neural P systems and surfacelet transform. Knowledge-Based Systems, 196(105794), 1–12.

    Google Scholar 

  32. Li, B., Peng, H., & Wang, J. (2021a). A novel fusion method based on dynamic threshold neural P systems and nonsubsampled contourlet transform for multi-modality medical images. Signal Processing, 178(107793), 1–13.

    Google Scholar 

  33. Li, B., Peng, H., Luo, X., Wang, J., Song, X., Pérez-Jiménez, M. J., & Riscos-Núñez, A. (2021). Medical image fusion method based on coupled neural P systems in nonsubsampled shearlet transform domain. International Journal of Neural Systems, 31(1), 2050050 (1-17).

    Article  Google Scholar 

  34. Cavaliere, M., Ibarra, O. H., Păun, G., Egecioglu, O., Ionescu, M., & Woodworth, S. (2009). Asynchronous spiking neural P systems. Theoretical Computer Science, 410(24–25), 2352–2364.

    Article  MathSciNet  MATH  Google Scholar 

  35. Song, T., Zou, Q., Liu, X., & Zeng, X. (2015). Asynchronous spiking neural P systems with rules on synapses. Neurocomputing, 151, 1439–1445.

    Article  Google Scholar 

  36. Cabarle, F. G. C., Adorna, H. N., & Pérez-Jiménez, M. J. (2015). Asynchronous spiking neural P systems with structural plasticity. In: International Conference on unconventional computation and natural computation, Springer, 9252, 132–143.

  37. Ibarra, O. H., Woodworth, S., Yu, F., & Păun, A. (2006). On spiking neural P systems and partially blind counter machines. In: International Conference on Unconventional Computation, Springer, 4135, 113–129.

  38. Ibarra, O. H., Păun, A., & Rodríguez-Patón, A. (2009). Sequential SNP systems based on min/max spike number. Theoretical Computer Science, 410(30–32), 2982–2991.

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang, X., Luo, B., Fang, X., & Pan, L. (2012). Sequential spiking neural P systems with exhaustive use of rules. BioSystems, 108(1–3), 52–62.

    Article  Google Scholar 

  40. Zhang, X., Zeng, X., Luo, B., & Pan, L. (2014). On some classes of sequential spiking neural P systems. Neural Computation, 26(5), 974–997.

    Article  MathSciNet  MATH  Google Scholar 

  41. Song, T., Pan, L., Jiang, K., Song, B., & Chen, W. (2013). Normal forms for some classes of sequential spiking neural P systems. IEEE Transactions on Nanobioscience, 12(3), 255–264.

    Article  Google Scholar 

  42. Jiang, K., Song, T., & Pan, L. (2013). Universality of sequential spiking neural P systems based on minimum spike number. Theoretical Computer Science, 499, 88–97.

    Article  MathSciNet  MATH  Google Scholar 

  43. Cabarle, F. G. C., Adorna, H. N., & Pérez-Jiménez, M. J. (2016). Sequential spiking neural P systems with structural plasticity based on max/min spike number. Neural Computing and Applications, 27(5), 1337–1347.

    Article  Google Scholar 

  44. Bao, T., Zhou, N., Lv, Z., Peng, H., & Wang, J. (2020). Sequential dynamic threshold neural P systems. Journal of Membrane Computing, 2, 255–268.

    Article  MathSciNet  MATH  Google Scholar 

  45. Peng, H., Yang, J., Wang, J., Wang, T., Sun, Z., Song, X., Luo, X., & Huang, X. (2017). Spiking neural P systems with multiple channels. Neural Networks, 95, 66–71.

    Article  MATH  Google Scholar 

  46. Song, X., Peng, H., Wang, J., Ning, G., Wang, T., Sun, Z., & Xia, Y. (2018). On small universality of spiking neural P systems with multiple channels. In: International Conference on Membrane Computing, Springer, 378, 229–245.

  47. Song, X., Wang, J., Peng, H., Ning, G., Sun, Z., Wang, T., & Yang, F. (2018b). Spiking neural P systems with multiple channels and anti-spikes. Biosystems, 169, 13–19.

    Article  Google Scholar 

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Acknowledgements

The authors thank the anonymous reviewers for providing very insightful and constructive suggestions, which have greatly help improve the presentation of this paper.

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Correspondence to Hong Peng.

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This work was partially supported by the National Natural Science Foundation of China (No. 62076206 and No. 62176216), China.

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Lv, Z., Yang, Q., Peng, H. et al. Computational power of sequential spiking neural P systems with multiple channels. J Membr Comput 3, 270–283 (2021). https://doi.org/10.1007/s41965-021-00089-9

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