Abstract
Automatic design of P systems is an attractive research topic in the community of membrane computing. Differing from the previous work that used evolutionary algorithms to fulfill the task, this paper presents the design of a (deterministic transition) P system (without input membrane) of degree 1, capturing the value of an arbitrary k-order (\(k\ge 2\)) polynomial p(n) by using a reasoning method. Specifically, the values of p(n) corresponding to a natural number t is equal to the multiplicity of a distinguished object of the system (the output object) in the configuration at instant t. We also discuss the descriptive computational resources required by the designed k-order polynomial P system.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Alhazov A, Martín-Vide C, Pan L (2003) Solving a pspace-complete problem by recognizing P systems with restricted active membranes. Fundam Inform 58(2):67–77
Chen Y, Zhang G, Wang T, Huang X (2014) Automatic design of a p system for basic arithmetic operations. Chin J Electron 23(2):302–304
Escuela G, Gutiérrez-Naranjo MA (2010) An application of genetic algorithms to membrane computing. In: Proceedings of the 8th brainstorming week on membrane computing. Fénix Editora, Sevilla, Spain, pp 101–108
He J, Xiao J, Liu X, Wu T, Song T (2015) A novel membrane-inspired algorithm for optimizing solid waste transportation. Optik Int J Light Electron Optics 126(23):3883–3888
Huang X, Zhang G, Rong H, Ipate F (2011) Evolutionary design of a simple membrane system. In: Gheorghe M, Paun G, Rozenberg G, Salomaa A, Verlan S (eds) Proceedings of international conference on membrane computing. Springer, Lecture Notes in Computer Science, vol 7184, pp 203–214
Liu X, Suo J, Leung SCH, Liu J, Zeng X (2015) The power of time-free tissue P systems: attacking np-complete problems. Neurocomputing 159:151–156
Ou Z, Zhang G, Wang T, Huang X (2013) Automatic design of cell-like p systems through tuning membrane structures, initial objects and evolution rules. Int J Unconv Comput 9(5–6):425–443
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
Păun G (2000) Computing with membranes. J Comput Syst Sci 61(1):108–143
Păun G, Rozenberg G, Salomaa AE (2010) The Oxford Handbook of membrane computing. Oxford University Press, New York
Song T, Macías-Ramos LF, Pan L, Pérez-Jiménez MJ (2014) Time-free solution to SAT problem using P systems with active membranes. Theoret Comput Sci 529:61–68
Song T, Zou Q, Liu X, Zeng X (2015) Asynchronous spiking neural P systems with rules on synapses. Neurocomputing 151:1439–1445
Tudose C, Lefticaru R, Ipate F (2011) Using genetic algorithms and model checking for p systems automatic design. In: Pelta DA, Krasnogor N, Dumitrescu D, Chira C, Lung RI (eds) Studies in computational intelligence, vol 387. NICSO, Springer, New York, pp 285–302
Wang X, Zhang G, Neri F, Jiang T, Gheorghe M, Ipate F, Lefticaru R (2016) Design and implementation of membrane controllers for trajectory tracking of nonholonomic wheeled mobile robots. Integr Comput Aided Eng 23:15–30
Xiao J, Huang Y, Cheng Z, He J, Niu Y (2014) A hybrid membrane evolutionary algorithm for solving constrained optimization problems. Optik 125(2):897–902
Zhang G, Cheng J, Gheorghe M, Meng Q (2013) A hybrid approach based on differential evolution and tissue membrane systems for solving constrained manufacturing parameter optimization problems. Appl Soft Comput 13(3):1528–1542
Zhang G, Gheorghe M, Pan L, Pérez-Jiménez MJ (2014a) Evolutionary membrane computing: a comprehensive survey and new results. Inf Sci 279:528–551
Zhang G, Rong H, Neri F, Pérez-Jiménez MJ (2014b) An optimization spiking neural P system for approximately solving combinatorial optimization problems. Int J Neural Syst 24(5):Article No. 1440,006
Zhang G, Rong H, Ou Z, Pérez-Jiménez MJ, Gheorghe M (2014c) Automatic design of deterministic and non-halting membrane systems by tuning syntactical ingredients. IEEE Trans Nanobiosci 13(3):363–371
Zhang G, Cheng J, Wang T, Wang X, Zhu J (2015) Membrane computing: theory and applications. Science Press, Beijing
Zhang X, Liu Y, Luo B, Pan L (2014d) Computational power of tissue P systems for generating control languages. Inf Sci 278:285–297
Acknowledgments
The work of W. Yuan, G. Zhang, T. Wang and Z. Huang is supported by the National Natural Science Foundation of China (61170016, 61373047). The work of M.J. Pérez-Jiménez is supported by Project TIN2012-37434 of the Ministerio de Economía y Competitividad of Spain, cofinanced by FEDER funds.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yuan, W., Zhang, G., Pérez-Jiménez, M.J. et al. P systems based computing polynomials: design and formal verification. Nat Comput 15, 591–596 (2016). https://doi.org/10.1007/s11047-016-9577-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11047-016-9577-y