Universality of spiking neural P systems with polarizations working in sequential mode induced by maximum spike number
Tóm tắt
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].
Tài liệu tham khảo
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.
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.
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.
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.
Fan, S., Paul, P., Wu, T., Rong, H., & Zhang, G. (2020). On applications of spiking neural P systems. Applied Sciences, 10(20), 7011.
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.
Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Single neurons, populations, plasticity. Cambridge University Press.
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.
Hertz, J., Krogh, A., & Palmer, R. G. (2018). Introduction to the theory of neural computation. CRC Press.
Ibarra, O. H., Păun, A., & Rodríguez-Patón, A. (2009). Sequential SNP systems based on min/max spike number. Theoretical Computer Science, 410, 2982–2991.
Ionescu, M., Păun, G., & Yokomori, T. (2006). Spiking neural P systems. Fundamenta Informaticae, 71(2—-3), 279–308.
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.
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.
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.
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.
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.
Li, J., Huang, Y., & Xu, J. (2016). Decoder design based on spiking neural P systems. IEEE Transactions on Nanobioscience, 15(7), 639–644.
Maass, W. (1997). Networks of spiking neurons: the third generation of neural network models. Neural Networks, 10(9), 1659–1671.
Maass, W. (1997). The Third generation of neural network models. Technische Universitat Gräz.
Maass, W., & Bishop, C. M. (2001). Pulsed neural networks. MIT Press.
Neary, T. (2015). Three small universal spiking neural P systems. Theoretical Computer Science, 567, 2–20.
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.
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.
Pan, L., & Zeng, X. (2011). Small universal spiking neural P systems working in exhaustive mode. IEEE Transactions on NanoBioscience, 10(2), 99–105.
Pan, T., Shi, X., Zhang, Z., & Xu, F. (2018). A small universal spiking neural P system with communication on request. Neurocomputing, 275, 1622–1628.
Păun, A., & Păun, G. (2007). Small universal spiking neural P systems. BioSystems, 90(1), 48–60.
Păun, G. (2000). Computing with membranes. Journal of Computer and System Sciences, 61(1), 108–143.
Păun, G. (2002). Membrane computing: An introduction. Springer-Verlag.
Păun, G. (2010). A quick introduction to membrane computing. The Journal of Logic and Algebraic Programming, 79(6), 291–294.
Păun, G., Rozenberg, G., & Salomaa, A. (2010). The Oxford handbook of membrane computing. Oxford University Press.
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.
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.
Song, T., & Pan, L. (2016). Spiking neural P systems with request rules. Neurocomputing, 193, 193–200.
Song, T., Pan, L., & Păun, G. (2013). Asynchronous spiking neural P systems with local synchronization. Information Sciences, 219, 197–207.
Song, T., Pan, L., & Păun, G. (2014). Spiking neural P systems with rules on synapses. Theoretical Computer Science, 529, 82–95.
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.
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.
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.
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.
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.
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.
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.
Wu, T., Pan, L., & Alhazov, A. (2019). Computation power of asynchronous spiking neural P systems with polarizations. Theoretical Computer Science, 777, 474–489.
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.
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.
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.
Wu, T., Zhang, Z., Păun, G., & Pan, L. (2016). Cell-like spiking neural P systems. Theoretical Computer Science, 623, 180–189.
Zeng, X., Xu, L., Liu, X., & Pan, L. (2014). On languages generated by spiking neural P systems with weights. Information Sciences, 278, 423–433.
Zhang, G., Pérez-Jiménez, M. J., & Gheorghe, M. (2017). Real-life applications with membrane computing. Springer.
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.
Zhang, X., Zeng, X., & Pan, L. (2008). Smaller universal spiking neural P systems. Fundamenta Informaticae, 87(1), 117–136.
Zhang, X., Zeng, X., & Pan, L. (2009). On languages generated by asynchronous spiking neural P systems. Theoretical Computer Science, 410(26), 2478–2488.
Zhao, Y., Liu, X., & Wang, W. (2016). Spiking neural P systems with neuron division and dissolution. Plos One, 11(9), 0162882.
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.