Equivalence in knowledge representation: Automata, recurrent neural networks, and dynamical fuzzy systems

Proceedings of the IEEE

Volumn 87, Issue 9, 1999, Pages 1623-1640

  Giles, C Lee ^a   Omlin, Christian W ^b   Thornber, Karvel K ^a,c  

^a NEC LABORATORIES AMERICA   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c STELLENBOSCH UNIVERSITY   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FINITE AUTOMATA; FUZZY SETS; MATHEMATICAL MODELS; RECURRENT NEURAL NETWORKS; THEOREM PROVING; VLSI CIRCUITS;

DETERMINISTIC FINITE STATE AUTOMATA (DFA); DYNAMICAL FUZZY SYSTEMS; FUZZY FINITE STATE AUTOMATA (FFA);

KNOWLEDGE REPRESENTATION;

EID: 0033360022     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/5.784244     Document Type: Article

References (67)

1. C. L. Giles, R. sun, and J. M. Zurada, IEEE Trans. Neural Netw-orks (Special Issue on Neural Neru'orks and Hybrid Intelligent Models: Foundations, Theory, and Applications), vol. 9, pp. 721-723, Sept. 1998.
2. L. A. Bookman and R. Sun, Connection Sci. (Special Issue on Architectures for Integrating Symbolic and Neural Processes), vol. 5, nos. 3 and 4, 1993.
3. J. Hendler, "Developing hybrid symbolic/connectionist models," in Advances in Connectionist and Neural Computation Theory, J. Barnden and J. Pollack, Eds. Ablex, 1991.
4. V. Honavar and L. Uhr, Eds., Artificial Intelligence and Neural Neru'orks: Steps Toward Principled Integration. San Diego, CA: Academic, 1994.
5. R. Sun, "Learning, action, and consciousness: A hybrid approach toward modeling consciousness," Neural Networks, vol. 10, no. 7, pp. 1317-1332, 1997.
6. J. Bezdek, IEEE Trans. Neural Nehvorks (Special Issue on Fuzzy Logic and Neural Neru'orks), vol. 3, 1992.
7. C. S. Hermann, "A hybrid fuzzy-neural expert system for diagnosis," in Proc. 14th Int. Joint Conf. Artificial Intelligence, vol. I, 1995, pp. 494-502.
8. M. Palaniswami, Y. Attikiouzel, R. J. Marks, and D. Fogel, Eds., Computational Intelligence: A Dynamic System Perspective. Piscataway, NJ: IEEE Press, 1995.
9. N. Kasabov, Foundations of Neural Nenvorks, Fuzzy Systems, and Knowledge Engineering. Cambridge, MA: MIT Press, 1996.
10. L. Zadeh, "Fuzzy sets," Inform. Control, vol. 8, no. 3, pp. 338-353, 1965.
11. H. R. Berenji and P. Khedkar, "Learning and fine tuning fuzzy logic controllers through reinforcement," IEEE Trans. Neural Networks, vol. 3, pp. 724-740, Sept. 1992.
12. P. P. Bonissone, V. Badami, K. H. Chiang, P. S. Khedkar, K. W. Marcelle, and M. J. Schütten, "Industrial applications of fuzzy loaic at General Electric," Proc. IEEE, vol. 83, pp. 450-465, Mar. 1995.
13. S. Chiu, S. Chand, D. Moore, and A. Chaudhary, "Fuzzy logic for control of roll and moment for a flexible wing aircraft," IEEE Control Syst. Mag., vol. 11, pp. 42-48, Apr. 1991.
14. J. Corbin, "A fuzzy logic-based financial transaction system," Embedded Syst. Programming, vol. 7, no. 12, p. 24, 1994.
15. L. G. Franquelo and J. Chavez, "Fasy: A fuzzy-logic based tool for analog synthesis," IEEETrans. Computer-Aided Design, vol. 15, p. 705, July 1996.
16. T. L. Hardy, "Multi-objective decision-making under uncertainty fuzzy logic methods," NASA, Washington, DC, Tech. Rep. TM 106796, 1994.
17. W. J. M. Kickert and H. R. van Nauta Lemke, "Application of a fuzzy controller in a warm water plant," Atitoinatica, vol. 12, no. 4, pp. 301-308, 1976.
18. C. C. Lee, "Fuzzy logic in control systems: Fuzzy logic controller," IEEE Trans. Syst., Man, Cybern., vol. 20, pp. 404-435, Feb. 1990.
19. C. P. Pappis and E. H. Mamdani, "A fuzzy logic controller for a traffic junction," IEEE Trans. Syst., Man, Cybern., vol. SMC-7, pp. 707-717, Oct. 1977.
20. X. M. Yang and G. J. Kalambur, "Design for machining using expert system and fuzzy logic approach," J. Mater. Eng. . Performance, vol. 4, no. 5, p. 599, 1995.
21. C. M. Bishop, Neural Networks for Pattern Recognition. New York: Oxford, 1995.
22. A. Cichocki and R. Unbehauen, Eds., Neural Nern'orks for Optimization and Signal Processing. New York: Wiley, 1993.
23. S. Haykin, Neural Nenvorks, A Comprehensive Foundation. New York: Prentice-Hall, 1998.
24. H. T. Siegelmann and E. D. Sontag, "Ont he computational power of neural nets," J. Comput. Syst. Sci., vol. 50, no. 1, pp. 132-150, 1995.
25. H. T. Siegelmann, Neural Networks and Analog Computation: Beyond the Turing Limit. Boston, MA: Birkhauser, 1999.
26. C. L. Giles and M. Gori, Eds., Adaptive Processing of Sequences and Data Structures (Lecture Notes in Artificial Intelligence). New York: Springer Verlag, 1998.
27. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation. Reading, MA: AddisonWesley, 1979.
28. P. Ashar, S. Devadas, and A. R. Newton, Sequential Logic Synthesis. Norwell, MA: Kluwer, 1992.
29. S. C. Kleene, "Representation of events in nerve nets and finite automata," in Automata Studies, C. E. Shannon and J. McCarthy, Eds. Princeton, NJ: Princeton Univ. Press, 1956, pp. 3-42.
30. M. Minsky, Computation: Finite and Infinite Machines. Englewood Cliffs, NJ: Prentice-Hall, Inc., 1967, ch. 3, pp. 32-66.
31. L.-M. Fu, Neural Networks in Computer Intelligence. New York: McGraw-Hill, 1994.
32. E. S. Santos, "Maximin automata," Inform. Control, vol. 12, pp. 363-377, 1968.
33. L. Zadeh, "Fuzzy languages and their relation to human and machine intelligence," Electron. Res. Lab., Univ. California, Berkeley, Tech. Rep. ERL-M302, 1971.
34. B. Gaines and L. Kohout, "The logic of automata," Int. J. General Syst., vol. 2, pp. 191-208, 1976.
35. E. B. Kosmatopoulos and M. A. Christodoulou, "Neural networks for identification of fuzzy dynamical systems: An appliation to identification of vehicle highway systems," in Proc. 4th IEEE Mediterranean Symp. New Directions in Control and Automation, 1996, pp. 23-38.
36. S. I. Mensch and H. M. Lipp, "Fuzzy specification of finite state machines," in Proc. Europ. Design Automation Conf., 1990, pp. 622-626.
37. C. W. Omlin and C. L. Giles, "Extraction of rules from discretetime recurrent neural networks," Neural Nehvorks, vol. 9, no. 1, pp. 41-52, 1996.
38. R. Maclin and J. W. Shavlik, "Using knowledge-based neural networks to improve algorithms: Refining the chou-fasman algorithm for protein folding," Machine Learning, vol. 11, nos. 2-3, pp. 195-215, 1993.
39. J. Grantner and M. J. Patyra, "Synthesis and analysis of fuzzy logic finite state machine models," in Proc. 3rd IEEE Conf. Fuzzy Syst., vol. I, 1994, pp. 205-210.
40. E. Khan and F. Unal, "Recurrent fuzzy logic using neural networks," in Advances in Fuzzy Logic, Neural Netn-orks, and Genetic Algorithms (Lecture Notes in Artificial Intelligence), T. Furuhashi, Ed. New York: Springer Verlag, 1995.
41. C. W. Omlin and C. L. Giles, "Constructing deterministic finitestate automata in recurrent neural networks," J. ACM, vol. 43, no. 6, pp. 937-972, 1996.
42. F. E. Cellier and Y. D. Pan, "Fuzzy adaptive recurrent counterpropagation neural networks: A tool for efficient implementation of qualitative models of dynamic processes," J. Syst. Eng., vol. 5, no. 4, pp. 207-222, 1995.
43. E. B. Kosmatopoulos and M. A. Christodoulou, "Structural properties of gradient recurrent high-order neural networks," IEEE Trans. Circuits Syst., vol. 42, pp. 592-603, Sept. 1995.
44. E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. loannou, "High-order neural networks for identification of dynamical systems," IEEE Trans. Neural Networks, vol. 6, pp. 422-431, Mar. 1995.
45. E. B. Kosmatopoulos and M. A. Christodoulou, "Recurrent neural networks for approximation of fuzzy dynamical systems," Int.J. Intell. Control Syst., vol. 1, no. 2, pp. 223-233, 1996.
46. M. P. Casey, "The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction," Neural Computation, vol. 8, no. 6, pp. 1135-1178, 1996.
47. A. Cleeremans, D. Servan-Schreiber, and J. McClelland, "Finite state automata and simple recurrent neural networks," Neural Computation, vol. 1, no. 3, pp. 372-381, 1989.
48. J. L. Elman, "Finding structure in time," Cognitive Sci., vol. 15, no. 2, pp. 179-211, 1990.
49. P. Frasconi, M. Gori, M. Maggini, and G. Soda, "Representation of finite state automata in recurrent radial basis function networks," Machine Learning, vol. 23, no. 1, pp. 5-32, 1996.
50. C. L. Giles, C. B. Miller, D. Chen, H. H. Chen, G. Z. Sun, and Y. C. Lee, "Learning and extracting finite state automata with second-order recurrent neural networks," Neural Computation, vol. 4, no. 3, pp. 393-105, 1992.
51. J. B. Pollack, "The induction of dynamical recognizres," Machine Learning, vol. 7, nos. 2/3, pp. 227-252, 1991.
52. R. L. Watrous and G. M. Kühn, "Induction of finite-state languages using second-order recurrent networks," Neural Computation, vol. 4, no. 3, pp. 406-411, 1992.
53. Z. Zeng, R. M. Goodman, and P. Smyth, "Learning finite state machines with self-clustering recurrent networks," Neural Computation, vol. 5, no. 6, pp. 976-990, 1993.
54. J. Grantner and M. J. Patyra, "VLSI implementations of fuzzy logic finite state machines," in Proc. 5th IFSA Congr., 1993, pp. 781-784.
55. F. A. Unal and E. Khan, "A fuzzy finite state machine implementation based on a neural fuzzy system," in Proc. 3rd Int. Conf. FiKzySyst., vol. 3, 1994, pp. 1749-1754.
56. C. W. Omlin, K. K. Thornber, and C. L. Giles, "Fuzzy finitestate automata can be deterministically encoded into recurrent neural networks," IEEE Trans. Fuzzy Syst., vol. 6, pp. 76-89, Feb. 1998.
57. A. Blanco, M. Delgado, and M. C. Pegalajar, "Fuzzy grammar inference using neural networks," Dep. Comput. Sci. Artificial Intell., Univ. Granada, Spain, Tech. Rep., 1997.
58. M. G. Thomason and P. N. Marinos, "Deterministic acceptors of regular fuzzy languages," IEEE Trans. Syst., Man, Cybern., vol. 4, pp. 228-230, Mar. 1974.
59. C. W. Omlin and C. L. Giles, "Stable encoding of large finite-state automata in recurrent neural networks with sigmoid discriminants," Neural Computation, vol. 8, no. 7, pp. 675-696, 1996.
60. L. A. Akers, D. K. Ferry, and R. O. Grondin, "Synthetic neural systems in VLSI," in An Introduction to Neural and Electronic Systems. San Diego, CA: Academic, 1990, pp. 317-336.
61. B. J. Sheu, Neural Information Processing and VLSI. Boston, MA: Kluwer, 1995.
62. C. Mead, Analog VLSI and Neural Systems. Reading, MA: Addison-Wesley, 1989.
63. C. L. Giles and C. W. Omlin, "Extraction, insertion and refinement of symbolic rules in dynamically driven recurrent neural networks," Connection Sci., vol. 5, nos. 3 & 4, pp. 307-337, 1993.
64. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications (Mathematics in Science and Engineering), vol. 144. New York: Academic, 1980, pp. 220-226.
65. S. F. Thomas, Fuzziness and Probability. Wichita, KS: ACG Press, 1995.
66. C. W. Omlin and C. L. Giles, "Rule revision with recurrent neural networks," IEEE Trans. Knowledge and Data Eng., vol. 8, pp. 183-188, Jan. 1996.
67. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.