Universal Memcomputing Machines

IEEE Transactions on Neural Networks and Learning Systems

Volumn 26, Issue 11, 2015, Pages 2702-2715

  Traversa, Fabio Lorenzo ^a   Di Ventra, Massimiliano ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brain; discrete Fourier transform (DFT); dynamic computing random access memory (DCRAM); elements with memory; fast Fourier transform (FFT); Fourier transform; memcomputing; memory; memristors; neural computing; nondeterministic polynomial (NP) complete; subset sum problem (SSP); Turing machine (TM).

Indexed keywords

BRAIN; DATA COMPRESSION; DATA STORAGE EQUIPMENT; DISCRETE FOURIER TRANSFORMS; DYNAMIC RANDOM ACCESS STORAGE; FAST FOURIER TRANSFORMS; FOURIER TRANSFORMS; HARDWARE; MACHINERY; MEMRISTORS; POLYNOMIAL APPROXIMATION; POLYNOMIALS; RANDOM ACCESS STORAGE;

MEMCOMPUTING; NEURAL COMPUTING; NONDETERMINISTIC POLYNOMIAL; RANDOM ACCESS MEMORY; SUBSET SUM PROBLEMS;

TURING MACHINES;

ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; COMPUTER SYSTEM; HUMAN; MEMORY;

COMPUTER SIMULATION; COMPUTER SYSTEMS; HUMANS; MEMORY; NEURAL NETWORKS (COMPUTER);

EID: 84945248040     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2015.2391182     Document Type: Article

References (48)

1. A. M. Turing, "On computational numbers, with an application to the entscheidungsproblem," Proc. London Math. Soc., vol. 42, no. 2, pp. 230-265, 1936.
2. A. M. Turing, The Essential Turing: Seminal Writings in Computing, Logic, Philosophy, Artificial Intelligence, and Artificial Life Plus the Secrets of Enigma, B. Jack Copeland, Ed. London, U.K.: Oxford Univ. Press, 2004.
3. S. Arora and B. Barak, Computational Complexity: A Modern Approach. Cambridge, U.K.: Cambridge Univ. Press, 2009.
4. J. von Neumann, "First draft of a report on the EDVAC," IEEE Ann. History Comput., vol. 15, no. 4, pp. 27-75, Oct./Dec. 1993.
5. J. Backus, "Can programming be liberated from the von Neumann style?: A functional style and its algebra of programs," Commun. ACM, vol. 21, no. 8, pp. 613-641, Aug. 1978.
6. J. L. Hennessy and D. A. Patterson, Computer Architecture: A Quantitative Approach, 4th ed. San Mateo, CA, USA: Morgan Kaufmann, 2006.
7. J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips, "GPU computing," Proc. IEEE, vol. 96, no. 5, pp. 879-899, May 2008.
8. W. Maass, T. Natschläger, and H. Markram, "Real-time computing without stable states: A new framework for neural computation based on perturbations," Neural Comput., vol. 14, no. 11, pp. 2531-2560, Nov. 2002.
9. M. Di Ventra and Y. V. Pershin, "The parallel approach," Nature Phys., vol. 9, pp. 200-202, Apr. 2013.
10. Y. V. Pershin, S. La Fontaine, and M. Di Ventra, "Memristive model of amoeba learning," Phys. Rev. E, vol. 80, p. 021926, Aug. 2009.
11. F. L. Traversa, Y. V. Pershin, and M. Di Ventra, "Memory models of adaptive behavior," IEEE Trans. Neural Netw. Learn. Syst., vol. 24, no. 9, pp. 1437-1448, Sep. 2013.
12. A. Bofill-i-Petit and A. F. Murray, "Synchrony detection and amplification by silicon neurons with STDP synapses," IEEE Trans. Neural Netw., vol. 15, no. 5, pp. 1296-1304, Sep. 2004.
13. Y. V. Pershin and M. Di Ventra, "Solving mazes with memristors: A massively parallel approach," Phys. Rev. E, vol. 84, p. 046703, Oct. 2011.
14. Y. V. Pershin and M. Di Ventra, "Self-organization and solution of shortest-path optimization problems with memristive networks," Phys. Rev. E, vol. 88, p. 013305, Jul. 2013.
15. T. Driscoll et al., "Memory metamaterials," Sci., vol. 325, no. 5947, pp. 1518-1521, 2009.
16. Y. V. Pershin and M. Di Ventra, "Memory effects in complex materials and nanoscale systems," Adv. Phys., vol. 60, no. 2, pp. 145-227, 2011.
17. M. Di Ventra and Y. V. Pershin, "On the physical properties of memristive, memcapacitive and meminductive systems," Nanotechnology, vol. 24, no. 25, p. 255201, 2013.
18. M. Di Ventra, Y. V. Pershin, and L. O. Chua, "Circuit elements with memory: Memristors, memcapacitors, and meminductors," Proc. IEEE, vol. 97, no. 10, pp. 1717-1724, Oct. 2009.
19. D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, "The missing memristor found," Nature, vol. 453, pp. 80-83, May 2008.
20. R. Waser and M. Aono, "Nanoionics-based resistive switching memories," Nature Mater., vol. 6, no. 11, pp. 833-840, 2007.
21. S. H. Jo, K.-H. Kim, and W. Lu, "Programmable resistance switching in nanoscale two-terminal devices," Nano Lett., vol. 9, no. 1, pp. 496-500, 2009.
22. A. Chanthbouala et al., "A ferroelectric memristor," Nature Mater., vol. 11, pp. 860-864, Sep. 2012.
23. H. O. Sillin et al., "A theoretical and experimental study of neuromorphic atomic switch networks for reservoir computing," Nanotechnology, vol. 24, no. 38, p. 384004, 2013.
24. Y. V. Pershin, V. A. Slipko, and M. Di Ventra, "Complex dynamics and scale invariance of one-dimensional memristive networks," Phys. Rev. E, vol. 87, p. 022116, Feb. 2013.
25. E. N. Oskoee and M. Sahimi, "Electric currents in networks of interconnected memristors," Phys. Rev. E, vol. 83, p. 031105, Mar. 2011.
26. M. W. Shihong, T. Prodromakis, I. Salaoru, and C. Toumazou. (Jun. 2012). "Modelling of current percolation channels in emerging resistive switching elements." [Online]. Available: http://arxiv.org/abs/1206.2746
27. R. K. Budhathoki, M. P. D. Sah, C. Yang, H. Kim, and L. Chua, "Transient behaviors of multiple memristor circuits based on flux charge relationship," Int. J. Bifurcation Chaos, vol. 24, no. 2, p. 1430006, 2014.
28. J. Borghetti, G. S. Snider, P. J. Kuekes, J. J. Yang, D. R. Stewart, and R. Stanley Williams, "'Memristive' switches enable 'stateful' logic operations via material implication," Nature, vol. 464, no. 7290, pp. 873-876, 2010.
29. Y. V. Pershin and M. Di Ventra, "Neuromorphic, digital and quantum computation with memory circuit elements," Proc. IEEE, vol. 100, no. 6, pp. 2071-2080, Jun. 2012.
30. M. Soltiz, D. Kudithipudi, C. Merkel, G. S. Rose, and R. E. Pino, "Memristor-based neural logic blocks for nonlinearly separable functions," IEEE Trans. Comput., vol. 62, no. 8, pp. 1597-1606, Aug. 2013.
31. A. Adamatzky and L. Chua, Eds., Memristor Networks. New York, NY, USA: Springer-Verlag, 2013.
32. F. L. Traversa, F. Bonani, Y. V. Pershin, and M. Di Ventra, "Dynamic computing random access memory," Nanotechnology, vol. 25, no. 28, p. 285201, 2014.
33. M. Itoh and L. O. Chua, "Memristor cellular automata and memristor discrete-time cellular neural networks," Int. J. Bifurcation Chaos, vol. 19, no. 11, pp. 3605-3656, 2009.
34. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. New York, NY, USA: Freeman, 1990.
35. S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd ed. Upper Saddle River, NJ, USA: Prentice-Hall, 1998.
36. M. Milev and M. Hristov, "Analog implementation of ANN with inherent quadratic nonlinearity of the synapses," IEEE Trans. Neural Netw., vol. 14, no. 5, pp. 1187-1200, Sep. 2003.
37. F. Bonani, F. Cappelluti, S. D. Guerrieri, and F. L. Traversa, "Harmonic balance simulation and analysis," in Wiley Encyclopedia of Electrical and Electronics Engineering. New York, NY, USA: Wiley, 2014.
38. D. Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer," Proc. Roy. Soc. London, A, Math. Phys. Sci., vol. 400, no. 1818, pp. 97-117, Jul. 1985.
39. P. W. Shor, "Algorithms for quantum computation: Discrete logarithms and factoring," in Proc. 35th Annu. Symp. Found. Comput. Sci., Nov. 1994, pp. 124-134.
40. P. W. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM J. Comput., vol. 26, no. 5, pp. 1484-1509, 1997.
41. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Information and the Natural Sciences), 10th ed. Cambridge, U.K.: Cambridge Univ. Press, 2010.
42. D. O. Hebb, The Organization of Behavior: A Neuropsychological Theory. New York, NY, USA: Wiley, May 1949.
43. P. T. Kohonen, Self-Organization and Associative Memory, 3rd ed. New York, NY, USA: Springer-Verlag, 1989.
44. E. S. Parker, L. Cahill, and J. L. McGaugh, "A case of unusual autobiographical remembering," Neurocase, vol. 12, no. 1, pp. 35-49, Feb. 2006.
45. A. K. R. LePort et al., "Behavioral and neuroanatomical investigation of highly superior autobiographical memory (HSAM)," Neurobiol. Learn. Memory, vol. 98, no. 1, pp. 78-92, Jul. 2012.
46. T. M. Cover and J. A. Thomas, Elements of Information Theory (Telecommunications and Signal Processing), 2nd ed. New York, NY, USA: Wiley, 2006.
47. G. Goertzel, "An algorithm for the evaluation of finite trigonometric series," Amer. Math. Monthly, vol. 65, no. 1, pp. 34-35, 1958.
48. S. Dasgupta, C. H. Papadimitriou, and U. Vazirani, Algorithms. New York, NY, USA: McGraw-Hill, 2008.