Abstract
This chapter presents different existing implementations of P systems using FPGA hardware. It gives the strong and the weak points of each implementation. A particular attention is given to the latest implementation of generalized numerical P systems that considers many advanced techniques. At the end of the chapter, a discussion about the challenges and the necessity of an FPGA implementation is performed.
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An integer or fixed-point encoded real is a bit vector.
References
C. Buiu, A.G. Florea, Membrane Computing models and robot controller design, current results and challenges. J. Membr. Comput. 1(4), 262–269 (2019). https://doi.org/10.1007/s41965-019-00029-8
N. Chomsky, M. Schützenberger. The algebraic theory of context-free languages, in Computer Programming and Formal Systems, Studies in Logic and the Foundations of Mathematics, ed. by P. Braffort, D. Hirschberg, vol. 35 (1963), pp. 118–161
D. Díaz-Pernil, M.A. Gutiérrez-Naranjo, H. Peng, Membrane computing and image processing: a short survey. J. Membr. Comput. 1(1), 58–73 (2019). https://doi.org/10.1007/s41965-018-00002-x
FPNtoVerilog GitHub repository. https://github.com/sverlan/FPNtoVerilog
R. Freund, A. Leporati, G. Mauri, A.E. Porreca, S. Verlan, C. Zandron, Flattening in (tissue) P systems, in Membrane Computing. CMC 2013, ed. by A. Alhazov, S. Cojocaru, M. Gheorghe, Y. Rogozhin, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 8340, pp. 173–188 (2013). https://doi.org/10.1007/978-3-642-54239-8_13
R. Freund, S. Verlan. A formal framework for static (tissue) P systems, in Membrane Computing. WMC 2007, ed. by G. Eleftherakis, P. Kefalas, Gh. Păun, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 4860 (2007), pp. 271–284. https://doi.org/10.1007/978-3-540-77312-2_17
R. Freund, S. Verlan, (tissue) P systems working in the k-restricted minimally or maximally parallel transition mode. Nat. Comput. 10(2), 821–833 (2011). https://doi.org/10.1007/s11047-010-9215-z
M. Gheorghe, F. Ipate, R. Lefticaru, C. Dragomir, An integrated approach to P systems formal verification, in Membrane Computing. CMC 2010, ed. by M. Gheorghe, T. Hinze, Gh. Păun, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 6501 (2010), pp. 226–239. https://doi.org/10.1007/978-3-642-18123-8_18
S. Ginsburg, E.H. Spanier, Semigroups, presburger formulas, and languages. Pac. J. Math. 16(2), 285–296 (1966). https://projecteuclid.org/euclid.pjm/1102994974
A. Leporati, A.E. Porreca, C. Zandron, G. Mauri, Improved universality results for parallel enzymatic numerical P systems. Int. J. Unconv. Comput. 9(5–6), 385–404 (2013)
B. Li, H. Peng, J. Wang, X. Huang, Multi-focus image fusion based on dynamic threshold neural P systems and surfacelet transform. Knowl. Based Syst. 196, 105794 (2020). https://doi.org/10.1016/j.knosys.2020.105794
G.H. Mealy, A method for synthesizing sequential circuits. Bell Syst. Tech. J. 34(5), 1045–1079 (1955). https://doi.org/10.1002/j.1538-7305.1955.tb03788.x
E.F. Moore, Gedanken-experiments on sequential machines, Automata Studies, ed. by C. E. Shannon, J. McCarthy. Annals of Mathematics Studies, vol. 34, litho-printed (Princeton University Press, Princeton 1956), pp. 129–153
V.T.T. Nguyen, Implementation of the Parallelism, Distribution and Nondeterminism of Membrane Computing Models on Reconfigurable Hardware. Ph.D. thesis
V.T.T. Nguyen, D. Kearney, G. Gioiosa, An algorithm for non-deterministic object distribution in P systems and its implementation in hardware, in Membrane Computing. WMC 2008, D.W. Corne, P. Frisco, Gh. Păun, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 5391 (2008), pp. 325–354. https://doi.org/10.1007/978-3-540-95885-7_24
V.T.T. Nguyen, D. Kearney, G. Gioiosa, An implementation of membrane computing using reconfigurable hardware. Comput. Inf. 27(3+ ), 551–569 (2008)
V.T.T. Nguyen, D. Kearney, G. Gioiosa, A region-oriented hardware implementation for Membrane Computing applications, in Membrane Computing. WMC 2009, ed. by Gh. Păun, M.J. Pérez-Jiménez, A. Riscos, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 5957 (2010), pp. 385–409. https://doi.org/10.1007/978-3-642-11467-0_27
R. Nicolescu, Parallel and distributed algorithms in P systems, in Membrane Computing. CMC 2011, ed. by M. Gheorghe, Gh. Păun, G. Rozenberg, A. Salomaa, S. Verlan. Lecture Notes in Computer Science, vol. 7184 (2011), pp. 35–50. https://doi.org/10.1007/978-3-642-28024-5_4
L. Pan, Gh. Păun, B. Song, Flat maximal parallelism in P systems with promoters. Theor. Comput. Sci. 623, 83–91 (2016). https://doi.org//10.1016/j.tcs.2015.10.027
Gh. Păun, Membrane Computing: An Introduction (Springer, Berlin, 2002)
Gh. Păun, R.A. Păun, Membrane computing and economics: numerical P systems. Fundam. Inf. 73(1–2), 213–227 (2006)
Gh. Păun, G. Rozenberg, A. Salomaa (eds.), The Oxford Handbook of Membrane Computing (Oxford University Press, Oxford, 2010)
A.B. Pavel, O. Arsene, C. Buiu, Enzymatic numerical P systems: a new class of membrane computing systems, in 2010 IEEEFifth International Conference on Bio-Inspired Computing: Theories and Applications, BIC-TA 2010, Changsha, China, September 23–26 (2010), pp. 1331–1336. https://doi.org/10.1109/BICTA.2010.5645071
A.B. Pavel, C. Buiu, Using enzymatic numerical P systems for modeling mobile robot controllers. Nat. Comput. 11(3), 387–393 (2012). https://doi.org/10.1007/s11047-011-9286-5
A.B. Pavel, C.I. Vasile, I. Dumitrache, Robot localization implemented with enzymatic numerical P systems, in Biomimetic and Biohybrid Systems. Living Machines 2012, ed. by T.J. Prescott, N.F. Lepora, A. Mura, P.F.M.J. Verschure. Lecture Notes in Computer Science, vol. 7375. Barcelona, Spain, July 9–12, 2012 (2012), pp. 204–215. https://doi.org/10.1007/978-3-642-31525-1_18
B. Petreska, C. Teuscher, A reconfigurable hardware membrane system, in Membrane Computing. WMC 2003, ed. by C. Martín-Vide, G. Mauri, Gh. Păun, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 2933 (2003), pp. 269–285. https://doi.org/10.1007/978-3-540-24619-0_20
J. Quirós, Implementación sobre hardware reconfigurable de una arquitectura no determinista, paralela y distribuida de alto rendimiento, basada en modelos de computación con membranas. Ph.D. thesis, Universidad de Sevilla, 2015 (in Spanish). http://hdl.handle.net/11441/39088
J. Quirós, S. Verlan, J. Viejo, A. Millán, M.J. Bellido, Fast hardware implementations of static P systems. Comput. Inf. 35(3), 687–718 (2016)
Z. Shang, S. Verlan, G. Zhang, Hardware implementation of numerical P systems, in Proceedings of the 20th International Conference on Membrane Computing, CMC20, ed. by Gh. Păun, August 5–8, 2019, Curtea de Arges, Romania (2019), pp. 463–474.
Z. Shang, S. Verlan, G. Zhang, H. Rong, FPGA implementation of numerical P systems. Int. J. Unconven. Comput. 16 (2021, in press)
C.E. Shannon, The synthesis of two-terminal switching circuits. Bell Syst. Tech. J. 28(1), 59–98 (1949). https://doi.org/10.1002/j.1538-7305.1949.tb03624.x
S. Verlan, Using the formal framework for P systems, in Membrane Computing. CMC 2013, ed. by A. Alhazov, S. Cojocaru, M. Gheorghe, Y. Rogozhin, G. Rozenberg, A. Salomaa. Lecture Notes in Computer Science, vol. 8340 (2013), pp. 56–79. https://doi.org/10.1007/978-3-642-54239-8_6
S. Verlan, J. Quirós, Fast hardware implementations of P systems, in Membrane Computing, CMC 2012, ed. by E. Csuhaj-Varjú, M. Gheorghe, G. Rozenberg, A. Salomaa, G. Vaszil. Lecture Notes in Computer Science, vol. 7762 (2012), pp. 404–423. https://doi.org/10.1007/978-3-642-36751-9_27
G. Zhang, Z. Shang, S. Verlan, M.A. Martínez-del-Amor, C. Yuan, L. Valencia-Cabrera, M.J. Pérez-Jiménez, An overview of hardware implementation of membrane computing models. ACM Comput. Surv. 53(4), 90 (2020). https://doi.org/10.1145/3402456
Xilinx 7 Series FPGAs Packaging and PinoutProduct Specification. https://www.xilinx.com/support/documentation/user_guides/ug475_7Series_Pkg_Pinout.pdf
Xilinx 7 Series FPGAs Configurable Logic Block User Guide. https://www.xilinx.com/support/documentation/user_guides/ug474_7Series_CLB.pdf
Xilinx web site. https://www.xilinx.com/
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Zhang, G. et al. (2021). P Systems Implementation on FPGA. In: Membrane Computing Models: Implementations. Springer, Singapore. https://doi.org/10.1007/978-981-16-1566-5_7
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DOI: https://doi.org/10.1007/978-981-16-1566-5_7
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