Abstract
Spiking neural P system is a class of bio-inspired computing model; a feature of traditional SN P system is that the precise execution time of each rule plays a crucial role. However, the execution that each rule has a precise execution time does not coincide with the biological fact, since the execution time of biochemical reactions can vary because of external uncontrollable conditions. SN P systems that work independently from the values associated with the execution times of the rules were investigated in Pan et al. (Neural Comput 23(5):1320–1342, 2011). In this work, we give a time-free solution to integer factorization problem by SN P systems, which means the execution times of the rules specified by different time mappings have no influence on the correctness of the solution. Besides, we prove that the systems are constructed in a uniform manner.
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Cavaliere M (2012) Time-free solution to hard computational problems. In: 10th brainstorming week on membrane computing, pp 204–210, Sevilla
Cavaliere M, Sburlan D (2005) Time-independent P systems. In: Mauri G, Păun G, Jesús Pérez-Jímenez M, Rozenberg G, Salomaa A (eds) Membrane computing, WMC 2004. LNCS, vol 3365. Springer, Heidelberg, pp 239–258
Cavaliere M, Ibarra OH, Păun G, Egecioglu O, Ionescu M, Woodworth S (2009) Asynchronous spiking neural P systems. Theor Comput Sci 410(24):2352–2364
Chen H, Ionescu M, Ishdorj T, Păun A, Păun G, Pérez-Jiménez M (2008) Spiking neural P systems with extended rules: universality and languages. Nat Comput 7(2):147–166
Ionescu M, Păun G, Yokomori T (2006) Spiking neural P systems. Fundam Inform 71(2–3):279–308
Ishdorj TO, Leporati A, Pan L, Zeng X, Zhang X (2010) Deterministic solutions to QSAT and Q3SAT by spiking neural P systems with pre-computed resources. Theor Comput Sci 411(25):2345–2358
Leporati A, Zandron C, Ferretti C, Mauri G (2007) Solving numerical NP-complete problem with spiking neural P systems. In: Eleftherakis G, Kefalas P, Păun GH, Rozenberg G, Salomaa A (eds) Membrane computing, International Workshop, WMC8, Selected and Invited Papers, Lecture Notes in Computer Science, vol 4860. Springer, pp 336–352
Leporati A, Mauri G, Zandron C, Păun G, Pérez-Jiménez MJ (2009) Uniform solutions to SAT and subset sum by spiking neural P systems. Nat Comput 8(4):681–702
Pan L, Zeng X (2011) Small universal spiking neural P systems working in exhaustive mode. IEEE Trans NanoBioscience 10(2):99–105
Pan L, Păun G, Pérez-Jiménez MJ (2011) Spiking neural P systems with neuron division and budding. Sci China Inf Sci 54(8):1596–1607
Pan L, Zeng X, Zhang X (2011) Time-free spiking neural P systems. Neural Comput 23(5):1320–1342
Pan L, Wang J, Hoogeboom HJ (2012) Spiking neural P systems with astrocytes. Neural Comput 24(3):805–825
Pan L, Zeng X, Zhang X, Jiang Y (2012) Spiking neural P systems with weighted synapses. Neural Process Lett 35(1):13–27
Păun A, Păun G (2007) Small universal spiking neural P systems. BioSystems 90(1):48–60
Păun G (2000) Computing with membranes. J Comput Syst Sci 61(1):108–143
Păun G, Pérez-Jiménez MJ, Rozenberg G (2006) Spike trains in spiking neural P systems. Int J Found Comput Sci 17(04):975–1002
Păun G (2002) Membrane computing: an introduction. Springer, Berlin
Păun G, Rozenberg G, Salomaa A (2010) The Oxford handbook of membrane computing. Oxford University Press Inc, Oxford
Song T, Pan L, Wang J, Venkat I, Subramanian K, Abdullah R (2012) Normal forms of spiking neural P systems with anti-spikes. IEEE Trans Nanobioscience 11:352–359
Song T, Pan L, Păun G (2013) Asynchronous spiking neural P systems with local synchronization. Inf Sci 219:197–207
Song T, Wang X, Zheng H (2013) Time-free solution to hamilton path problems using P systems with d-division. J Appl Math. Article ID 975798, 7 pages, 2013. doi:10.1155/2013/975798
Song T, Luo L, He J, Chen Z, Zhang K (2014) Solving subset sum problems by time-free spiking neural P systems. Appl Math Inf Sci 8(1):327–332
Song T, Macías-Ramos LF, Pan L, Pérez-Jiménez MJ (2014) Time-free solution to SAT problem using P systems with active membranes. Theor Comput Sci 529:61–68
Wang J, Shi P, Peng H, Perez-Jimenez MJ, Wang T (2013) Weighted fuzzy spiking neural P systems. IEEE Trans Fuzzy Syst 21(2):209–220
Zeng X, Pan L, Pérez-Jiménez MJ (2014) Small universal simple spiking neural P systems with weights. Sci China Inf Sci 57(9):1–11
Zeng X, Xu L, Liu X, Pan L (2014) On languages generated by spiking neural P systems with weights. Inf Sci 278:423–433
Zeng X, Zhang X, Song T, Pan L (2014) Spiking neural P systems with thresholds. Neural Comput pp 1–22
Zhang G, Rong H, Neri F, Pérez-Jiménez MJ (2014) An optimization spiking neural P system for approximately solving combinatorial optimization problems. Int J Neural Syst 24(05):1–15
Zhang X, Zeng X, Pan L (2008) On string languages generated by spiking neural P systems with exhaustive use of rules. Nat Comput 7(4):535–549
Acknowledgments
The work was supported by National Natural Science Foundation of China (Grant Nos. 61472333, 51405408, 61370010 and 71103154), China Scholarship Council (201308350065), Natural Science Foundation of Fujian Province of China (No. 2011J01334, 2014J01253), Base Research Project of Shenzhen Bureau of Science, Technology, and Information (JCYJ20120618155655087, JC201006030858A).
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Liu, X., Li, Z., Suo, J. et al. A uniform solution to integer factorization using time-free spiking neural P system. Neural Comput & Applic 26, 1241–1247 (2015). https://doi.org/10.1007/s00521-014-1799-2
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DOI: https://doi.org/10.1007/s00521-014-1799-2