Abstract
Cell-like spiking neural P systems (abbreviated as cSN P systems) are a class of distributed and parallel computation devices which combine a hierarchical arrangement of membranes in rewriting P systems and evolution rules in spiking neural P systems. The existing results show that cSN P systems are Turing universal with replication target indication or general spiking rules that produce more spikes than the ones consumed. However, with neither the replication target indication nor general spiking rules, cSN P systems can only compute finite set of numbers. In this work, we introduce evolution rules into cSN P systems to compensate the loss of computation power, the application of which depends on the contents of a region. With an evolution rule, every copy of spike evolves to a designate multiset over one kind of objects. We prove that cSN P systems with evolution rules are computationally universal in the case of using traditional spiking rules while avoiding the replication target indication. We also investigate the influence of the target indications on the computation power of cSN P systems with evolution rules. The results show that removing some target indications has no influence on computation power but a corresponding increase in the number of membranes. Besides, the results give a solution to the open problem that seeks alternative methods for the replication of spikes in a cSN P system.
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References
Bernardini F, Gheorghe M (2005) Cell communication in tissue P systems: universality results. Soft Comput 9(9):640–649
Cavaliere M (2003) Evolution-communication P systems. In: Păun G, Rozenberg G, Salomaa A, Zandron C (eds) Membrane computing. WMC 2002. Lecture notes in computer science, vol 2597. Springer, Berlin
Cavaliere M, Ibarra OH, Păun G, Egecioglu O, Ionesc M, Woodworth S (2009) Asynchronous spiking neural P systems. Theor Comput Sci 410(24):2352–2364
Chen H, Freund R, Ionescu M, Pérez-Jiménez MJ (2007) On string languages generated by spiking neural P systems. Fundam Inf 75(1):141–162
Díaz-Pernil D, Peña-Cantillana F, Gutiérrez-Naranjo MA (2013) A parallel algorithm for skeletonizing images by using spiking neural P systems. Neurocomputing 115:81–91
Dorigo M, Bonabeau E, Theraulaz G (2000) Ant algorithms and stigmergy. Future Gener Comput Syst 16(8):851–871
Fahmi A, Abdullah S, Amin F, Ali A (2017a) Precursor selection for sol–gel synthesis of titanium carbide nanopowders by a new cubic fuzzy multi-attribute group decision-making model. J Intell Syst
Fahmi A, Abdullah S, Amin F, Siddiqui N (2017b) Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. J Intell Fuzzy Syst 33(6):3323–3337
Fahmi A, Abdullah S, Amin F, Ali A (2018a) Weighted average rating (war) method for solving group decision making problem using triangular cubic fuzzy hybrid aggregation (tcfha). Punjab Univ J Math 50(1):23–34
Fahmi A, Abdullah S, Amin F, Ahmed R, Ali A (2018b) Triangular cubic linguistic hesitant fuzzy aggregation operators and their application in group decision making. J Intell Fuzzy Syst 34(4):2401–2416
Freund R, Păun A (2005) P systems with active membranes and without polarizations. Soft Comput 9(9):657–663
Frisco P, Gheorghe M, Pérez-Jiménez MJ (2014) Applications of membrane computing in systems and synthetic biology. Springer, Berlin
García-Quismondo M, Levin M, Lobo D (2017) Modeling regenerative processes with membrane computing. Inf Sci 381:229–249
Hopcroft JE, Motwani R, Ullman JD (2001) Introduction to automata theory, languages, and computation, 3rd edn. Addison Wesley, Pearson Education India, New Jersey
Ibarra OH, Păun A, Păun G, Rodríguez-Patón A, Sosík P, Woodworth S (2007) Normal forms for spiking neural P systems. Theor Comput Sci 372(2–3):196–217
Ibarra OH, Woodworth S (2006) Characterizations of some restricted spiking neural P systems. In: Hoogeboom HJ, Păun G, Rozenberg G, Salomaa A (eds) Membrane computing, vol 4361. Springer, Berlin, pp 424–442
Ionescu M, Păun G, Yokomori T (2006) Spiking neural P systems. Fund Inf 71(2):279–308
Ionescu M, Păun G, Yokomori T (2007) Spiking neural P systems with an exhaustive use of rules. Int J Unconv Comput 3(2):135–153
Jain Anil K, Duin Robert P (2000) Statistical pattern recognition: a review. IEEE Trans Pattern Anal Mach Intell 22(1):4–37
Korec I (1996) Small universal register machines. Theor Comput Sci 168:267–301
Maass W (1997) Networks of spiking neurons: the third generation of neural network models. Neural Netw 10(9):1659–1671
Manca V, Bianco L (2008) Biological networks in metabolic P systems. BioSystems 91(3):489–498
Martin-Vide C, Pazos J, Păun G (2003) Tissue P systems. Theor Comput Sci 296(2):295–326
Minsky M (1967) Computation: finite and infinite machines. Prentice-Hall, Englewood Cliffs
Neary T (2010) A boundary between universality and non-universality in extended spiking neural P systems. In: Dediu A-H, Fernau H, Martín-Vide C (eds) Language and automata theory and applications. Springer, Berlin, pp 475–487
Păun G (2000) Computing with membranes. J Comput Syst Sci 61(1):108–143
Păun G (2001) P systems with active membranes: attacking NP-complete problems. J Autom Lang Comb 6:75–90
Păun G (2002) Membrane computing: an introduction. Springer, Berlin
Păun G, Păun R (2006) Membrane computing and economics: numerical P systems. Fund Inf 73(1–2):213–227
Păun A, Păun G (2007) Small universal spiking neural P systems. BioSystems 90(1):48–60
Păun G, Rozenberg G (2002) A guide to membrane computing. Theor Comput Sci 287(1):73–100
Păun G, Pérez-Jiménez MJ, Pazos J, Rodríguez-Patón A (2005) Symport/antiport P systems with three objects are universal. Fund Inf 64(1–4):353–367
Păun G, Rozenberg G, Salomaa A (2010) The Oxford handbook of membrane computing. Oxford University Press, New York
Peng H, Wang J, Pérez-Jiménez MJ, Wang H, Shao J, Wang T (2013) Fuzzy reasoning spiking neural P systems for fault diagnosis. Inf Sci 235:106–116
Song B, Pérez-Jiménez MJ, Pan L (2015a) Computational efficiency and universality of timed P systems with membrane creation. Soft Comput 19(11):3043–3053
Song T, Xu J, Pan L (2015b) On the universality and non-universality of spiking neural P systems with rules on synapses. IEEE Trans NanoBiosci 14(8):960–966
Song B, Pan L, Pérez-Jiménez MJ (2016) Cell-like P systems with channel states and symport/antiport rules. IEEE Trans Nanobiosci 15(6):555–566
Song B, Zhang C, Pan L (2017) Tissue-like P systems with evolutional symport/antiport rules. Inf Sci 378(1):177–193
Stephens M, Smith NJ, Donnelly P (2001) A new statistical method for haplotype reconstruction from population data. Am J Hum Genet 68(4):978–989
Wu T, Zhang Z, Pan L (2016a) On languages generated by cell-like spiking neural P systems. IEEE Trans NanoBiosci 15(5):455–466
Wu T, Zhang Z, Păun G, Pan L (2016b) On the universality of colored one-catalyst P systems. Fund Inf 144(2):205–212
Wu T, Zhang Z, Păun G, Pan L (2016c) Cell-like spiking neural P systems. Theor Comput Sci 623:180–189
Zeng X, Xu L, Liu X, Pan L (2014) On languages generated by spiking neural P systems with weights. Inf Sci 278:423–433
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(5):1–16
Acknowledgements
This work was supported by National Natural Science Foundation of China (61320106005, 61472154, and 61502186) and China Postdoctoral Science Foundation (2016M592335).
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Pan, T., Xu, J., Jiang, S. et al. Cell-like spiking neural P systems with evolution rules. Soft Comput 23, 5401–5409 (2019). https://doi.org/10.1007/s00500-018-3500-7
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DOI: https://doi.org/10.1007/s00500-018-3500-7