Small Universal Spiking Neural P Systems with Homogenous Neurons and Synapses

• Autorzy: Wu T. , Wang Y. , Jiang S. , Shi X.

Identyfikatory

DOI

10.3233/FI-2016-1456

• Języki publikacji: EN

Abstrakty

EN

Spiking neural (SN, for short) P systems are a class of distributed parallel computing models inspired by the way in which neurons communicate with each other by means of electrical impulses. Recently, a new variant of SN P systems, called SN P systems with homogenous neurons and synapses (HRSSN P systems for short) was proposed, where the spiking and forgetting rules are placed on synapses instead of in neurons and each synapse has the same set of spiking and forgetting rules. This variant of SN P systems has already been proved to be Turing universal as both number generating and accepting devices. In this work, we consider the problem of looking for small universal HRSSN P systems. Specifically, a universal HRRSN P system with standard rules and weight at most 5 having 70 neurons is constructed as a device of computing functions; as a number generator, we find a universal system with standard rules and weight at most 5 having 71 neurons.

Słowa kluczowe

EN

bio-inspired computing; membrane computing; small universal system; spiking neural p system; turing completeness

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 149, nr 4
• Strony: 451--470
• Opis fizyczny: Bibliogr. 58 poz., rys., tab.

Twórcy

autor

Wu T.

• Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China

autor

Wang Y.

• School of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

autor

Jiang S.

• School of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

autor

Shi X.

• Key Laboratory of Image Information Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China

Bibliografia

• [1] Hagan MT, Demuth HB, Beale MH, De Jesús O. Neural network design (2nd Edition). PWS Publishing Co. Boston, MA, USA; 1996. ISBN-13:978-0-9717321-1-7.
• [2] Ghosh-Dastidar S, Adeli H. Spiking neural networks. International Journal of Neural Systems. 2009; 19(04):295–308. doi:10.1142/S0129065709002002.
• [3] Chen X, Pérez-Jiménez MJ, Valencia-Cabrera L, Wang B, Zeng X. Computing with viruses. Theoretical Computer Science. 2016;623:146–159. doi:10.1016/j.tcs.2015.12.006.
• [4] Ionescu M, Păun G, Yokomori T. Spiking neural P systems. Fundamenta Informaticae. 2006;71(2–3):279–308. Available from: http://dl.acm.org/citation.cfm?id=1227505.1227513.
• [5] Păun G, Rozenberg G, Salomaa A, editors. The Oxford Handbook of Membrane Computing. New York: Oxford University Press; 2010. ISBN:0199556679.
• [6] Chen H, Freund R, Ionescu M, Păun G, Pérez-Jiménez MJ. On string languages generated by spiking neural P systems. Fundamenta Informaticae. 2007;75(1–4):141–162. Available from: http://fi.mimuw.edu.pl/index.php/FIhttp://content.iospress.com/journals/fundamenta-informaticae/145/2.
• [7] Chen H, Ionescu M, Ishdorj TO, Păun A, Păun G, Pérez-Jiménez M. Spiking neural P systems with extended rules: universality and languages. Natural Computing. 2008;7(2):147–166. doi:10.1007/s11047-006-9024-6.
• [8] Păun A, Păun G. Small universal spiking neural P systems. BioSystems. 2007;90(1):48–60. doi:10.1016/j.biosystems.2006.06.006.
• [9] Zhang X, Zeng X, Pan L. Smaller universal spiking neural P systems. Fundamenta Informaticae. 2008; 87(1):117–136. Available from: http://dl.acm.org/citation.cfm?id=2366091.2366099.
• [10] Leporati A, Mauri G, Zandron C, Păun G, Pérez-Jiménez MJ. Uniform solutions to SAT and Subset Sum by spiking neural P systems. Natural Computing. 2008;8(4):681–702. doi:10.1007/s11047-008-9091-y.
• [11] Pan L, Păun G, Pérez-Jiménez MJ. Spiking neural P systems with neuron division and budding. Science China Information Sciences. 2011;54(8):1596–1607. doi:10.1007/s11432-011-4303-y.
• [12] Ishdorj TO, Leporati A, Pan L, Zeng X, Zhang X. Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources. Theoretical Computer Science. 2010;411(25):2345–2358. doi:10.1016/j.tcs.2010.01.019.
• [13] Pan L, Păun G. Spiking neural P systems with anti-spikes. International Journal of Computers Communications & Control. 2009;4(3):273–282. doi:10.1.1.488.3781.
• [14] Song T, Pan L, Wang J, Venkat I, Subramanian K, Abdullah R. Normal forms of spiking neural P systems with anti-spikes. IEEE Transactions on NanoBioscience. 2012;11(4):352–359. doi:10.1109/TNB.2012.2208122.
• [15] Zeng X, Zhang X, Song T, Pan L. Spiking neural P systems with thresholds. Neural Computation. 2014;26(7):1340–1361. doi:10.1162/NECO_a_00605.
• [16] Song T, Pan L, Păun G. Spiking neural P systems with rules on synapses. Theoretical Computer Science. 2014;529:82–95. doi:10.1016/j.tcs.2014.01.001.
• [17] Song T, Pan L. Spiking neural P systems with rules on synapses working in maximum spikes consumption strategy. IEEE Transactions on NanoBioscience. 2015;14(1):38–44. doi:10.1109/TNB.2014.2367506.
• [18] Cabarle FGC, Adorna HN, Pérez-Jiménez MJ, Song T. Spiking neural P systems with structural plasticity. Neural Computing and Applications. 2015;26(8):1905–1917. doi:10.1007/s00521-015-1857-4.
• [19] Zhang X, Pan L, Păun A. On the universality of axon P systems. IEEE Transactions on Neural Networks and Learning Systems. 2015;26(11):2816–2829. doi:10.1109/TNNLS.2015.2396940.
• [20] Wu T, Zhang Z, Păun G, Pan L. Cell-like spiking neural P systems. Theoretical Computer Science. 2016;623:180–189. doi:10.1016/j.tcs.2015.12.038.
• [21] Cavaliere M, Ibarra OH, Păun G, Egecioglu O, Ionescu M, Woodworth S. Asynchronous spiking neural P systems. Theoretical Computer Science. 2009;410(24):2352–2364. doi:10.1016/j.tcs.2009.02.031.
• [22] Song T, Pan L, Păun G. Asynchronous spiking neural P systems with local synchronization. Information Sciences. 2013;219:197–207. doi:10.1016/j.ins.2012.07.023.
• [23] Ibarra OH, Păun A, Rodríguez-Patón A. Sequential SNP systems based on min/max spike number. Theoretical Computer Science. 2009;410(30):2982–2991. doi:10.1016/j.tcs.2009.03.004.
• [24] Jiang K, Song T, Pan L. Universality of sequential spiking neural P systems based on minimum spike number. Theoretical Computer Science. 2013;499:88–97. doi:10.1016/j.tcs.2013.07.006.
• [25] Cabarle FGC, Adorna HN, Pérez-Jiménez MJ. Sequential spiking neural P systems with structural plasticity based on max/min spike number. Neural Computing and Applications. 2015;p. 1–11. doi:10.1007/s00521-015-1937-5.
• [26] Ionescu M, Păun G, Yokomori T. Spiking neural P systems with an exhaustive use of rules. International Journal of Unconventional Computing. 2007;3(2):135–153. Available from: http://www.oldcitypublishing.com/IJUC/IJUCabstracts/IJUC3.2abstracts/IJUCv3n2p135-153Ionescu.html.
• [27] Zhang X, Wang B, Pan L. Spiking neural P systems with a generalized use of rules. Neural Computation. 2014;26(12):2925–2943. doi:10.1162/NECO_a_00665.
• [28] Zhang G, Rong H, Neri F, Pérez-Jiménez MJ. An optimization spiking neural P system for approximately solving combinatorial optimization problems. International Journal of Neural Systems. 2014;24(5):1–16. doi:10.1142/S0129065714400061.
• [29] Peng H, Wang J, Pérez-Jiménez MJ, Wang H, Shao J, Wang T. Fuzzy reasoning spiking neural P systems for fault diagnosis. Information Sciences. 2013;235:106–116. doi:10.1016/j.ins.2012.07.015.
• [30] Wang J, Shi P, Peng H, Pérez-Jiménez MJ, Wang T. Weighted fuzzy spiking neural P systems. IEEE Transactions on Fuzzy Systems. 2013;21(2):209–220. doi:10.1109/TFUZZ.2012.2208974.
• [31] Díaz-Pernil D, Peña-Cantillana F, Gutiérrez-Naranjo MA. A parallel algorithm for skeletonizing images by using spiking neural P systems. Neurocomputing. 2013;115:81–91. doi:10.1016/j.neucom.2012.12.032.
• [32] Wang T, Zhang G, Zhao J, He Z, Wang J, Pérez-Jiménez MJ. Fault diagnosis of electric power systems based on fuzzy reasoning spiking neural P systems. IEEE Transactions on Power Systems. 2015; 30(3):1182–1194. doi:10.1109/TPWRS.2014.2347699.
• [33] Gutiérrez-Naranjo MÁ, Leporati A. First steps towards a CPU made of spiking neural P systems. International Journal of Computers Communications & Control. 2009;5(3):244–252. doi:10.15837/ijccc.2009.3.2432.
• [34] Liu X, Li Z, Liu J, Liu L, Zeng X. Implementation of Arithmetic Operations With Time-Free Spiking Neural P Systems. IEEE Transactions on NanoBioscience. 2015;14(6):617–624. doi:10.1109/TNB.2015.2438257.
• [35] Macías-Ramos LF, Pérez-Hurtado I, García-Quismondo M, Valencia-Cabrera L, Pérez-Jiménez MJ, Riscos-Núñez A. A P-Lingua based simulator for spiking neural P systems. In: Proceedings of the 12th International Conference on Membrane Computing, August 23-26, 2011, Fontainebleau, France, M. Gheorghe et al. (eds.). vol. 7184. LNCS, Springer; 2012. p. 257–281. ISBN:978-3-642-28023-8. doi:10.1007/978-3-642-28024-5_18.
• [36] Macías-Ramos LF, Pérez-Jiménez MJ, Song T, Pan L. Extending Simulation of Asynchronous Spiking Neural P Systems in P-Lingua. Fundamenta Informaticae. 2015;136(3):253–267. doi:10.3233/FI-2015-1156.
• [37] Cabarle FG, Adorna H, Martínez-del Amor MA, Pérez-Jiménez MJ. Spiking neural P system simulations on a high performance GPU platform. In: Algorithms and Architectures for Parallel Processing, Y. Xiang et al. (eds.). vol. 7017. LNCS, Springer; 2011. p. 99–108. ISBN:978-3-642-24668-5. doi:10.1007/978-3-642-24669-2_10.
• [38] Cabarle FGC, Adorna H, Martínez-del Amor MA. A spiking neural P system simulator based on CUDA. In: Proceedings of the 12th International Conference on Membrane Computing, August 23-26, 2011, Fontainebleau, France, M. Gheorghe et al. (eds.). vol. 7184. LNCS, Springer; 2012. p. 87–103. ISBN:978-3-642-28023-8. doi:10.1007/978-3-642-28024-5_18.
• [39] Rogozhin Y. Small universal Turing machines. Theoretical Computer Science. 1996;168(2):215–240. doi:10.1016/S0304-3975(96)00077-1.
• [40] Korec I. Small universal register machines. Theoretical Computer Science. 1996;168(2):267–301. doi:10.1016/S0304-3975(96)00080-1.
• [41] Siegelmann HT, Sontag ED. On the computational power of neural nets. Journal of Computer and System Sciences. 1995;50(1):132–150. doi:10.1006/jcss.1995.1013.
• [42] Pan L, Zeng X. A note on small universal spiking neural P systems. In: Proceedings of the 10th International Workshop on Membrane Computing, August 24-27, 2009, Curtea de Argeş, Romania, Păun G. et al. (eds.). vol. 5957. LNCS, Springer; 2009. p. 436–447. doi:10.1007/978-3-642-11467-0_29.
• [43] Neary T. Three small universal spiking neural P systems. Theoretical Computer Science. 2015;567:2–20. doi:10.1016/j.tcs.2014.09.006.
• [44] Pan L, Zeng X, Zhang X, Jiang Y. Spiking neural P systems with weighted synapses. Neural Processing Letters. 2012;35(1):13–27. doi:10.1007/s11063-011-9201-1.
• [45] Zeng X, Zhang X, Pan L. Homogeneous spiking neural P systems. Fundamenta Informaticae. 2009; 97(1):275–294. doi:10.3233/FI-2009-200.
• [46] Păun A, Sosík P. Three universal homogeneous spiking neural P systems using max spike. Fundamenta Informaticae. 2014;134(1-2):167–182. doi:10.3233/FI-2014-1097.
• [47] Jiang K, Chen W, Zhang Y, Pan L. Spiking neural P systems with homogeneous neurons and synapses. Neurocomputing. 2016;171:1548–1555. doi:10.1016/j.neucom.2015.07.097.
• [48] Rozenberg G, Salomaa A, editors. Handbook of Formal Languages. vol. 1–3. Berlin: Springer-Verlag; 1997. ISBN:978-3-662-07675-0.
• [49] Minsky ML. Computation: Finite and Infinite Machines. Prentice–Hall, Englewood Cliffs, N.J.; 1967. ISBN-13:978-0131655638.
• [50] Jiang K, Song T, Chen W, Pan L. Homogeneous spiking neural P systems working in sequential mode induced by maximum spike number. International Journal of Computer Mathematics. 2013;90(4):831–844. doi:10.1080/00207160.2012.737462.
• [51] Song T, Pan L. Spiking neural P systems with rules on synapses working in maximum spiking strategy. IEEE Transactions on NanoBioscience. 2015;14(4):465–477. doi:10.1109/TNB.2014.2367506.
• [52] Song T, Wang X, Zhang Z, Chen Z. Homogenous spiking neural P systems with anti-spikes. Neural Computing and Applications. 2014;24(7-8):1833–1841. doi:10.1007/s00521-013-1397-8.
• [53] Păun G. Membrane Computing. An Introduction. In: Natural Computing Series. Springer-Verlag, Berlin; 2002. doi:10.1007/978-3-642-56196-2.
• [54] Wang J, Hoogeboom HJ, Pan L, Păun G, Pérez-Jiménez MJ. Spiking neural P systems with weights. Neural Computation. 2010;22(10):2615–2646. doi:10.1162/NECO_a_00022.
• [55] Zhang X, Zeng X, Pan L. On languages generated by asynchronous spiking neural P systems. Theoretical Computer Science. 2009;410(26):2478–2488. doi:10.1016/j.tcs.2008.12.055.
• [56] Ionescu M, Sburlan D. Some applications of spiking neural P systems. Computing and Informatics. 2012;27(3):515–528.
• [57] Zeng X, Xu L, Liu X, Pan L. On languages generated by spiking neural P systems with weights. Information Sciences. 2014;278:423–433. doi:10.1016/j.ins.2014.03.062.
• [58] Zhang X, Zeng X, Pan L. Weighted spiking neural P systems with rules on synapses. Fundamenta Informaticae. 2014;134(1-2):201–218. doi:10.3233/FI-2014-1099.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).