Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 236806, 8 pages
http://dx.doi.org/10.1155/2015/236806
Research Article

Simulation of Turing Machine with uEAC-Computable Functions

1School of Automation, Beijing Institute of Technology, Beijing 100081, China
2Department of Electrical and Computer Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA

Received 10 June 2015; Accepted 3 November 2015

Academic Editor: Jean J. Loiseau

Copyright © 2015 Yilin Zhu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Freeth, Y. Bitsakis, X. Moussas et al., “Decoding the ancient Greek astronomical calculator known as the antikythera mechanism,” Nature, vol. 444, no. 7119, pp. 587–591, 2006. View at Publisher · View at Google Scholar · View at Scopus
  2. C. E. Shannon, “Mathematical theory of the differential analyzer,” Journal of Mathematics and Physics, vol. 20, pp. 337–354, 1941. View at Publisher · View at Google Scholar · View at MathSciNet
  3. V. Bush, “The differential analyzer. A new machine for solving differential equations,” Journal of the Franklin Institute, vol. 212, no. 4, pp. 447–488, 1931. View at Publisher · View at Google Scholar · View at Scopus
  4. L. A. Rubel, “The extended analog computer,” Advances in Applied Mathematics, vol. 14, no. 1, pp. 39–50, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. J. Mycka, “Analog computation beyond the turing limit,” Applied Mathematics and Computation, vol. 178, no. 1, pp. 103–117, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. D. S. Graca, M. L. Campagnolo, and J. Buescu, “Computability with polynomial differential equations,” Advances in Applied Mathematics, vol. 40, no. 3, pp. 330–349, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  7. M. Piekarz, “The extended analog computer and functions computable in a digital sense,” Acta Cybernetica, vol. 19, no. 4, pp. 749–764, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. W. Mills, B. Himebaug, A. Allred et al., “Extended analog computers: a unifying paradigm for VLSI, plastic and colloidal computing systems,” in Proceedings of the Workshop on Unique Chips and Systems (UCAS-1). Held in Conjunction with IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS '05), Austin, Tex, USA, 2005.
  9. J. W. Mills, M. Parker, B. Himebaugh, C. Shue, B. Kopecky, and C. Weilemann, “‘Empty space’ computes: the evolution of an unconventional supercomputer,” in Proceedings of the 3rd Conference on Computing Frontiers (CF '06), pp. 115–126, Como, Italy, May 2006. View at Publisher · View at Google Scholar · View at Scopus
  10. J. W. Mills, “The nature of the extended analog computer,” Physica D, vol. 237, no. 9, pp. 1235–1256, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. W. Mills, M. G. Beavers, and C. A. Daffinger, “Lukasiewicz logic arrays,” in Proceedings of the 20th International Symposium on Multiple-Valued Logic, pp. 4–10, Charlotte, NC, USA, May 1990. View at Publisher · View at Google Scholar
  12. J. W. Mills and C. A. Daffinger, “CMOS VLSI Lukasiewicz logic arrays,” in Proceedings of the International Conference on Application Specific Array Processors, pp. 469–480, Princeton, NJ, USA, September 1990. View at Scopus
  13. J. W. Mills, T. Walker, and B. Himebaugh, “Lukasiewicz' insect: continuous-valued robotic control after ten years,” Journal of Multiple-Valued Logic and Soft Computing, vol. 9, no. 2, pp. 131–146, 2003. View at Google Scholar · View at Scopus
  14. B. Himebaugh, “Design of eac,” 2005, http://www.cs.indiana.edu/~bhimebau/.
  15. J. W. Mills, “The continuous retina: image processing with a single-sensor artificial neural field network,” in Proceedings of the IEEE International Conference on Neural Networks, vol. 2, pp. 886–891, IEEE, Washington, DC, USA, June 1996. View at Publisher · View at Google Scholar
  16. M. Parker, C. Zhang, J. W. Mills, and B. Himebaugh, “Evolving letter recognition with an extended analog computer,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '06), pp. 609–614, IEEE, July 2006. View at Scopus
  17. F. Pan, R. Zhang, T. Long, and Z. Li, “The research on the application of uEAC in XOR problems,” in Proceedings of the International Conference on Transportation, Mechanical, and Electrical Engineering (TMEE '11), pp. 109–112, IEEE, Changchun, China, December 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Tsuda, J. Jones, A. Adamatzky, and J. Mills, “Routing physarum with electrical flow/current,” International Journal of Nanotechnology and Molecular Computation, vol. 3, no. 2, pp. 56–70, 2011. View at Publisher · View at Google Scholar
  19. J. W. Mills, “Programmable vlsi extended analog computer for cyclotron beam control,” Tech. Rep., Indiana University, 1995. View at Google Scholar
  20. A. M. Turing, “On computable numbers, with an application to the entscheidungsproblem,” Proceedings London Mathematical Society, vol. s2-42, no. 1, pp. 230–265, 1937. View at Publisher · View at Google Scholar
  21. L. A. Rubel, “Some mathematical limitations of the general-purpose analog computer,” Advances in Applied Mathematics, vol. 9, no. 1, pp. 22–34, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. Y. Zhu, F. Pan, W. Li, Q. Gao, and X. Ren, “Optimization of multi-micro extended analog computer array and its applications to data mining,” International Journal of Unconventional Computing, vol. 10, no. 5-6, pp. 455–471, 2014. View at Google Scholar · View at Scopus
  23. H. T. Siegelmann and E. D. Sontag, “Analog computation via neural networks,” Theoretical Computer Science, vol. 131, no. 2, pp. 331–360, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. H. T. Siegelmann and E. D. Sontag, “On the computational power of neural nets,” Journal of Computer and System Sciences, vol. 50, no. 1, pp. 132–150, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  25. N. Ainslie, R. Baula, N. Deckard et al., “Toward the evolution of analog computers for control of data networks,” Tech. Rep., Indiana University, Indianapolis, Ind, USA, 2002. View at Google Scholar