Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A formal framework for spiking neural P systems

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

Abstract

Spiking neural P systems are a class of distributed parallel computing models, inspired by the way in which neurons process information and communicate with each other by means of spikes. In 2007, Freund and Verlan developed a formal framework for P systems to capture most of the essential features of P systems and to define their functioning in a formal way. In this work, we present an extension of the formal framework related to spiking neural P systems by considering the applicability of each rule to be controlled by specific conditions on the current contents of the cells. The main objective of this extension is to also capture spiking neural P systems in the formal framework. Another goal of our extension is to incorporate the notions of input and output. Finally, we also show that in the case of spiking neural P systems, the rules have a rather simple form and in that way spiking neural P systems correspond to vector addition systems where the application of rules is controlled by semi-linear sets.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Alhazov, A., Freund, R., Ivanov, S., Oswald, M., & Verlan, S. (2015). Extended spiking neural P systems with white hole rules. In Proceedings of the Thirteenth Brainstorming Week on Membrane Computing (pp. 45–62). Sevilla, ETS de Ingeniería Informática, 2–6 de Febrero, 2015.

  2. Alhazov, A., Freund, R., Oswald, M., & Slavkovik, M. (2006). Extended spiking neural P systems. In H. J. Hoogeboom, Gh. Păun, G. Rozenberg, A. Salomaa (Eds.), Membrane Computing, 7th International Workshop, WMC 2006, Leiden, The Netherlands, July 17–21, 2006, Revised, Selected, and Invited Papers, Lecture Notes in Computer Science (Vol. 4361, pp. 123–134). Springer: Berlin. https://doi.org/10.1007/11963516_8

  3. Cabarle, F. G. C., Adorna, H. N., Jiang, M., & Zeng, X. (2017). Spiking neural P systems with scheduled synapses. IEEE Transactions on Nanobioscience, 16(8), 792–801.

    Article  Google Scholar 

  4. 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  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  6. Chen, H., Ionescu, M., Ishdorj, T. O., Păun, A., Păun, Gh, & Pérez-Jiménez, M. (2008). Spiking neural P systems with extended rules: Universality and languages. Natural Computing, 7(2), 147–166.

    Article  MathSciNet  Google Scholar 

  7. Csuhaj-Varjú, E., & Verlan, S. (2017). Bi-simulation between P colonies and P systems with multi-stable catalysts. In M. Gheorghe, G. Rozenberg, A. Salomaa, C. Zandron (Eds.), Membrane Computing - 18th International Conference, CMC 2017, Bradford, UK, July 25–28, 2017, Revised Selected Papers, Lecture Notes in Computer Science (Vol. 10725, pp. 105–117). Springer: Berlin.

  8. Freund, R. (2019). A general framework for sequential grammars with control mechanisms. In M. Hospodár, G. Jirásková, S. Konstantinidis (Eds.), Descriptional Complexity of Formal Systems - 21st IFIP WG 1.02 International Conference, DCFS 2019, Košice, Slovakia, July 17–19, 2019, Proceedings, Lecture Notes in Computer Science (Vol. 11612, pp. 1–34). Springer: Berlin. https://doi.org/10.1007/978-3-030-23247-4_1

  9. Freund, R., Ivanov, S., & Verlan, S. (2015). P systems with generalized multisets over totally ordered Abelian groups. In G. Rozenberg, A. Salomaa, J. M. Sempere, C. Zandron (Eds.), Membrane Computing - 16th International Conference, CMC 2015, Valencia, Spain, August 17–21, 2015, Revised Selected Papers, Lecture Notes in Computer Science (Vol. 9504, pp. 117–136). Springer: Berlin. https://doi.org/10.1007/978-3-319-28475-0_9

  10. Freund, R., Pérez-Hurtado, I., Riscos-Núñez, A., & Verlan, S. (2013). A formalization of membrane systems with dynamically evolving structures. International Journal of Computer Mathematics, 90(4), 801–815. https://doi.org/10.1080/00207160.2012.748899.

    Article  MathSciNet  MATH  Google Scholar 

  11. Freund, R., & Verlan, S. (2007). A formal framework for static (tissue) P systems. In G. Eleftherakis, P. Kefalas, Gh. Păun, G. Rozenberg, A. Salomaa (Eds.), Membrane Computing, 8th International Workshop, WMC 2007, Thessaloniki, Greece, June 25–28, 2007 Revised Selected and Invited Papers, Lecture Notes in Computer Science (Vol. 4860, pp. 271–284). Springer: Berlin. https://doi.org/10.1007/978-3-540-77312-2_17

  12. Freund, R., & Verlan, S. (2011). (tissue) P systems working in the k-restricted minimally or maximally parallel transition mode. Natural Computing, 10(2), 821–833.

    Article  MathSciNet  Google Scholar 

  13. 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  Google Scholar 

  14. Ibarra, O. H., Păun, A., Păun, Gh, Rodríguez-Patón, A., Sosík, P., & Woodworth, S. (2007). Normal forms for spiking neural P systems. Theoretical Computer Science, 372(2–3), 196–217. https://doi.org/10.1016/j.tcs.2006.11.025.

    Article  MathSciNet  MATH  Google Scholar 

  15. Ionescu, M., Păun, Gh, & Yokomori, T. (2007). Spiking neural P systems with an exhaustive use of rules. International Journal of Unconventional Computing, 3(2), 135–154.

    Google Scholar 

  16. Ionescu, M., Păun, Gh., Pérez Jiménez, M.d.J., & Rodríguez Patón, A. (2011). Spiking neural P systems with several types of spikes. In Proceedings of the Ninth Brainstorming Week on Membrane Computing (pp. 183–192). Sevilla, ETS de Ingeniería Informática. Fénix Editora.

  17. Ionescu, M., Păun, Gh, & Yokomori, T. (2006). Spiking neural P systems. Fundamenta Informaticae, 71(2–3), 279–308.

    MathSciNet  MATH  Google Scholar 

  18. 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  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  21. Pan, L., Păun, Gh, & Song, B. (2016). Flat maximal parallelism in P systems with promoters. Theoretical Computer Science, 623, 83–91. https://doi.org/10.1016/j.tcs.2015.10.027.

    Article  MathSciNet  MATH  Google Scholar 

  22. Pan, L., Wu, T., & Zhang, Z. (2016). A bibliography of spiking neural P systems. Bulletin of the International Membrane Computing Society, 1, 63–78.

    Google Scholar 

  23. Pan, L., Zeng, X., Zhang, X., & Jiang, Y. (2012). Spiking neural P systems with weighted synapses. Neural Processing Letters, 35(1), 13–27.

    Article  Google Scholar 

  24. Peng, H., & Wang, J. (2019). Coupled neural P systems. IEEE Transactions on Neural Networks and Learning Systems, 30(6), 1672–1682.

    Article  MathSciNet  Google Scholar 

  25. Peng, H., Yang, J., Wang, J., Wang, T., Sun, Z., Song, X., et al. (2017). Spiking neural P systems with multiple channels. Neural Networks, 95, 66–71. https://doi.org/10.1016/j.neunet.2017.08.003.

    Article  MATH  Google Scholar 

  26. Păun, Gh, Rozenberg, G., & Salomaa, A. (Eds.). (2010). The Oxford Handbook of Membrane Computing. Oxford, England: Oxford University Press.

    MATH  Google Scholar 

  27. Rong, H., Wu, T., Pan, L., & Zhang, G. (2018). Spiking neural P systems: Theoretical results and applications. In: C. G. Díaz, A. Riscos-Núñez, Gh. Păun, G. Rozenberg, A. Salomaa (Eds.), Enjoying Natural Computing - Essays Dedicated to Mario de Jesús Pérez-Jiménez on the Occasion of His 70th Birthday, Lecture Notes in Computer Science (Vol. 11270, pp. 256–268). Springer: Berlin. https://doi.org/10.1007/978-3-030-00265-7_20

  28. Song, T., Rodríguez-Patón, A., Zheng, P., & Zeng, X. (2017). Spiking neural P systems with colored spikes. IEEE Transactions on Cognitive and Developmental Systems, 10(4), 1106–1115.

    Article  Google Scholar 

  29. Song, X., Wang, J., Peng, H., Ning, G., Sun, Z., Wang, T., et al. (2018). Spiking neural P systems with multiple channels and anti-spikes. BioSystems, 169–170, 13–19. https://doi.org/10.1016/j.biosystems.2018.05.004.

    Article  Google Scholar 

  30. Verlan, S. (2013). Using the formal framework for P systems. In A. Alhazov, S. Cojocaru, M. Gheorghe, Yu. Rogozhin, G. Rozenberg, A. Salomaa (Eds.), Membrane Computing - 14th International Conference, CMC 2013, Chişinău, Republic of Moldova, August 20-23, 2013, Revised Selected Papers, Lecture Notes in Computer Science (Vol. 8340, pp. 56–79). Springer: Berlin. Invited paper

  31. Verlan, S., Freund, R., Alhazov, A., & Pan, L. (2019). A formal framework for spiking neural P systems. In Gh. Păun (Ed.), Proceedings of the 20th International Conference on Membrane Computing, CMC20, August 5–8, 2019, Curtea de Argeş, Romania (pp. 523–535).

  32. Verlan, S., & Quiros, J. (2012). Fast hardware implementations of P systems. In E. Csuhaj-Varjú, M. Gheorghe, G. Rozenberg, A. Salomaa, G. Vaszil (Eds.), Membrane Computing - 13th International Conference, CMC 2012, Budapest, Hungary, August 28-31, 2012, Revised Selected Papers, Lecture Notes in Computer Science (Vol. 7762, pp. 404–423). Springer: Berlin.

  33. Wang, J., Hoogeboom, H. J., Pan, L., Păun, Gh, & Pérez-Jiménez, M. J. (2010). Spiking neural P systems with weights. Neural Computation, 22(10), 2615–2646. https://doi.org/10.1162/NECO_a_00022.

    Article  MathSciNet  MATH  Google Scholar 

  34. 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 

  35. 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 

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

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The ideas for this paper were discussed during the stay of Artiom Alhazov and Rudolf Freund in Paris at Créteil with Sergey Verlan in summer 2018, while Rudolf Freund was a guest professor supported by the Université Paris Est Créteil.

Author information

Authors and Affiliations

  1. Univ Paris Est Creteil, LACL, F-94010, Creteil, France

    Sergey Verlan

  2. Faculty of Informatics, TU Wien, Favoritenstraße 9–11, 1040, Wien, Austria

    Rudolf Freund

  3. Vladimir Andrunachievici Institute of Mathematics and Computer Science, Academiei 5, MD-2028, Chişinău, Moldova

    Artiom Alhazov

  4. IBISC, Univ. Évry, Université Paris-Saclay, 23 Boulevard de France, 91025, Évry, France

    Sergiu Ivanov

  5. Key Laboratory of Image Information Processing and Intelligent Control of Education Ministry of China, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Linqiang Pan

Authors
  1. Sergey Verlan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rudolf Freund
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Artiom Alhazov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sergiu Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Linqiang Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sergey Verlan.

Ethics declarations

Conflicts of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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

Verlan, S., Freund, R., Alhazov, A. et al. A formal framework for spiking neural P systems. J Membr Comput 2, 355–368 (2020). https://doi.org/10.1007/s41965-020-00050-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41965-020-00050-2

Keywords

Search

Navigation