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Power Consumption in Cellular Automata

  • Georgios Ch. SirakoulisEmail author
  • Ioannis Karafyllidis
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 30)

Abstract

Cellular Automata (CAs) have been established as one of the most intriguing and efficient computational tools of our era with unique properties to fit well with the most of the upcoming nanotechnological and parallel computation aspects. Algorithms based on CAs are ideally suited for hardware implementation, due to their discreteness and their simple, regular and modular structure with local interconnections. On the other hand, power dissipation is considered as a rather limiting parameter for the advancement of high performance hardware design . In this chapter the undergoing relationship between CAs and the corresponding power consumption would be exploited as a matter of importance for their hardware design analysis with many promising aspects. First of all in order to establish a clear connection, a power estimation model for combinational logic circuits using CA and focused on glitching estimation will be presented to elucidate the application of CA model to hardware power dissipation measurements. Following that, the power consumption of CA based logic circuits and namely of 1-d CAs rules logic circuits will be analytically investigated. In particular, CMOS power consumption estimation measurements for all the Wolfram 1-d CAs rules as well as entropy variation measurements were conducted for various study cases and different initial conditions and the findings are discussed in detail and in terms of 1-d CAs rules categorization.

References

  1. 1.
    von Neumann, J.: Theory of self-reproducing automata. University of Illinois Press, Champaign (1966)Google Scholar
  2. 2.
    Ulam, S.: Random processes and transformations. Int. Congr. Math. 2, 264–275 (1952)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Wolfram, S.: Theory and applications of cellular automata. World Scientific, Singapore (1986)zbMATHGoogle Scholar
  4. 4.
    Wolfram, S.: Cellular automata as models of complexity. Nature 311, 419–424 (1984)CrossRefGoogle Scholar
  5. 5.
    Di Lena, P., Margara, L.: Computational complexity of dynamical systems: the case of cellular automata. Inf. Comput. Inf. Control 206, 1104–1116 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Hurley, M.: Attractors in cellular automata. Ergod. Theory Dyn. Syst. 10, 131–140 (1990)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Culik II, K., Hurd, L.P., Yu, S.: Computation theoretic aspects of cellular automata. Phys. D. Nonlinear Phenom. 45, 357–378 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 10, 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sirakoulis, G.Ch., Bandini, S.: Cellular automata. In: 10th International Conference on Cellular Automata for Research and Industry, ACRI 2012, Santorini Island, Greece, September 24–27, 2012. Proceedings. Lecture Notes in Computer Science. Springer, Berlin (2012)Google Scholar
  10. 10.
    Was, J., Sirakoulis, G.Ch., Bandini, S.: Cellular automata. In: 11th International Conference on Cellular Automata for Research and Industry, ACRI 2014, Krakow, Poland, September 22–25, 2014, Proceedings. Lecture Notes in Computer Science. Springer International Publishing, Berlin (2014)Google Scholar
  11. 11.
    Toffoli, T.: Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Physica D 10, 117–127 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Chaudhuri, P.P., Chaudhuri, D.R., Nandi, S., Chattopadhyay, S.: Theory and Applications: Additive Cellular Automata. IEEE Press, New York (1997)Google Scholar
  13. 13.
    Sirakoulis, G.Ch., Karafyllidis, I., Soudris, D., Georgoulas, N., Thanailakis, A.: A new simulator for the oxidation process in integrated circuit fabrication based on cellular automata. Model. Simul. Mater. Sci. Eng. 7(4), 631 (1999)Google Scholar
  14. 14.
    Sirakoulis, G.Ch., Karafyllidis, I., Thanailakis, A.: A cellular automaton methodology for the simulation of integrated circuit fabrication processes. Futur. Gener. Comput. Syst. 18(5), 639–657 (2002)Google Scholar
  15. 15.
    Tsompanas, M.-A.I., Sirakoulis, G.Ch., Adamatzky, A.I.: Evolving transport networks with cellular automata models inspired by slime mould. IEEE Trans. Cyber. 45(9), 1887–1899 (2015)Google Scholar
  16. 16.
    Dourvas, N.I., Sirakoulis, G.Ch.: Cellular automaton Belousov–Zhabotinsky model for binary full adder. Int. J. Bifurc. Chaos 27(06), 1750089 (2017)Google Scholar
  17. 17.
    Sirakoulis, G.Ch., Karafyllidis, I., Thanailakis, A.: A CAD system for the construction and VLSI implementation of cellular automata algorithms using VHDL. Microprocess. Microsyst. 27(8), 381–396 (2003)Google Scholar
  18. 18.
    Jendrsczok, J., Ediger, P., Hoffmann, R.: A scalable configurable architecture for the massively parallel GCA model. Int. J. Parallel Emerg. Distrib. Syst. 24, 275–291 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Georgoudas, I.G., Kyriakos, P., Sirakoulis, G.Ch., Andreadis, I.T.: An FPGA implemented cellular automaton crowd evacuation model inspired by the electrostatic-induced potential fields. Microprocess. Microsyst. 34(7), 285–300 (2010)Google Scholar
  20. 20.
    Tsompanas, M.-A.I., Sirakoulis, G.Ch.: Modeling and hardware implementation of an amoeba-like cellular automaton. Bioinspiration Biomim. 7(3), 036013 (2012)Google Scholar
  21. 21.
    Vourkas, I., Sirakoulis, G.Ch.: FPGA based cellular automata for environmental modeling. In: 2012 19th IEEE International Conference on Electronics, Circuits, and Systems (ICECS 2012), pp. 93–96 (2012)Google Scholar
  22. 22.
    Kalogeropoulos, G., Sirakoulis, G.Ch., Karafyllidis, I.: Cellular automata on FPGA for real-time urban traffic signals control. J. Supercomput. 65(2), 664–681 (2013)Google Scholar
  23. 23.
    Progias, P., Sirakoulis, G.Ch.: An FPGA processor for modelling wildfire spreading. Math. Comput. Model. 57(5), 1436–1452 (2013)Google Scholar
  24. 24.
    Mardiris, V., Sirakoulis, G.Ch., Mizas, C., Karafyllidis, I., Thanailakis, A.: A CAD system for modeling and simulation of computer networks using cellular automata. IEEE Trans. Syst. Man Cyber. Part C Appl. Rev. 38(2), 253–264 (2008)Google Scholar
  25. 25.
    Sirakoulis, G.Ch.: A TCAD system for VLSI implementation of the cvd process using VHDL. Int. VLSI J. 37(1), 63–81 (2004)Google Scholar
  26. 26.
    Georgoudas, I.G., Sirakoulis, G.Ch., Scordilis, E.M., Andreadis, I.T.: On-chip earthquake simulation model using potentials. Nat. Hazard. 50(3), 519–537 (2009)Google Scholar
  27. 27.
    Karafyllidis, I., Mavridis, S., Soudris, D., Thanailakis, A.: Estimation of power dissipation in glitching using complex-time cellular automata. In: 6th IEEE International Conference on Electronics, Circuits and Systems, vol. 3, pp. 1639–1642 (1999)Google Scholar
  28. 28.
    Sirakoulis, G.Ch., Karafyllidis, I.: Power estimation of 1-d cellular automata circuits. In: 2010 International Conference on High Performance Computing Simulation, pp. 691–697 (2010)Google Scholar
  29. 29.
    Sirakoulis, G.Ch., Karafyllidis, I.: Cellular automata and power consumption. J. Cell. Autom. 7(1), 67–80 (2012)Google Scholar
  30. 30.
    Weste, N., Harris, D.: CMOS VLSI Design: A Circuits And Systems Perspective, 4th edn. Addison-Wesley Publishing Company, USA (2010)Google Scholar
  31. 31.
    Kotoulas, L.G., Tsarouchis, D., Sirakoulis, G.Ch., Andreadis, I.: 1-d cellular automaton for pseudorandom number generation and its reconfigurable hardware implementation. In: IEEE International Symposium on Circuits and Systems, pp. 4627–4630 (2006)Google Scholar
  32. 32.
    Langton, C.G.: Computation at the edge of chaos: phase transitions and emergent computation. Phys. D 42, 12–37 (1990)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Gilman, R.H.: Classes of linear automata. Ergod. Theory Dyn. Syst. 7(1), 105118 (1987)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Gutowitz, H., Langton, C.: Mean field theory of the edge of chaos. In: Proceedings of ECAL3, pp. 52–64. Springer, Berlin (1995)Google Scholar
  35. 35.
    Adamatzky, A.: Identification of cellular automata. In: Encyclopedia of Complexity and Systems Science, pp. 4739–4751 (2009)Google Scholar
  36. 36.
    Eppstein, D.: Growth and decay in life-like cellular automata. In: Adamatzky, A. (ed.) Game of Life Cellular Automata, pp. 71–97. Springer, London (2010)Google Scholar
  37. 37.
    DAlotto, L.: A classification of one-dimensional cellular automata using infinite computations. Appl. Math. Comput. 255, 15–24 (2015). (Special issue devoted to the international conference Numerical computations: Theory and Algorithms June 1723, 2013. Falerna, Italy)Google Scholar
  38. 38.
    Zenil, H.: Compression-based investigation of the dynamical properties of cellular automata and other systems. CoRR (2009). arXiv:0910.4042

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Georgios Ch. Sirakoulis
    • 1
    Email author
  • Ioannis Karafyllidis
    • 1
  1. 1.Department of Electrical and Computer EngineeringDemocritus University of ThraceThraceGreece

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