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Automata theory based on complete residuated lattice-valued logic (II)

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Abstract

It reveals some equivalences between automata based on complete residuated lattice-valued logic (calledl valued automata) and the truth-value lattice of the underlying logic (i.e. residuated lattice). In particular, it demonstrates several basic equivalent characterizations on the retrievability ofl valued automata. Finally, the connections of the homomorphisms between twol valued automata to continuous mappings and open mappings are clarified. So this paper establishes further the more profound fuzzy automata theory.

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References

  1. Hopcroft, J. E., Ullman, J. D., Introduction to Automata Theory, Languages, and Computation, New York: Addison-Wesley, 1979, 13–223.

    MATH  Google Scholar 

  2. Alon, N., Dewdney, A., Ott, T., Efficient simulation of finite automata by neural nets, J. Assoc. Comput. Mach., 1991, 38(2): 498–514.

    MathSciNet  Google Scholar 

  3. Shen, E. S., Model-theoretic logic and theoretical computer science, Advances in Mathematics (in Chinese), 1996, 25(3): 193–202.

    MATH  MathSciNet  Google Scholar 

  4. Wee, W. G., On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. Thesis, Purdue University, June, 1967.

  5. Malik, D. S., Mordeson, J. N., Fuzzy Discrete Structures, New York: Physica-Verlag, 2000, 139–246.

    MATH  Google Scholar 

  6. Omlin, C. W., Thornber, K. K., Giles, C. L., Fuzzy Finite-state Automata Can Be Deterministically Encoded into Recurrent Neural Networks, IEEE Trans. Fuzzy Syst., 1998, 6(1): 76–89.

    Article  Google Scholar 

  7. Holcombe, W. M. L., Algebraic Automata Theory, New York: Cambridge University Press, 1982.

    MATH  Google Scholar 

  8. Bavel, Z., Introduction to the Theory of Automata, Virginia: Reston Publishing Company, Inc., 1983.

    MATH  Google Scholar 

  9. Qiu, D. W., Automata theory based on complete residuated lattice-valued logic, Science in China, Ser. F, 2001, 44(6): 419–429.

    Google Scholar 

  10. Wang, S. Q., Lu, J. B., The ultraproduct basic theorems of lattice-valued models, Chinese Science Bulletin, 1981, 26(2): 71–74.

    Google Scholar 

  11. Wang, S. Q., Two applications of constant constructive method in lattice-valued models theory, Chinese Science Bulletin, 1981, 26(3): 129–130.

    Google Scholar 

  12. Wang, S. Q., Omitting types theorem in lattice-valued models theory, Acta Mathematica Sinica (in Chinese), 1982, 25(2): 202–207.

    MATH  MathSciNet  Google Scholar 

  13. Shen, F. X., Elementary entension and elementary chain of lattice-valued models, Chinese Science Bulletin, 1982, 27(5): 264–266.

    MathSciNet  Google Scholar 

  14. Wang, G. J., Theory of L-Fuzzy Topological Spaces (in Chinese), Xi’an: Shaanxi Normal University Press, 1988.

    Google Scholar 

  15. Ying, M. S., Some of cover-style compactness in fuzzy topology, Acta Mathematica Sinica (in Chinese), 1994, 37(6): 852–856.

    MATH  MathSciNet  Google Scholar 

  16. Qiu, D. W., On cover-style fuzzy compactness (in chinese), Journal of Zhongshan University, 1998, 37(3): 46–49.

    MATH  Google Scholar 

  17. Pavelka, J., On fuzzy logic I, II, III, Zeitschr f math Logik und Grundlagen d Math, 1979, 25: 45–52; 119–134; 447–464.

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang, G. J., Non-classical Mathematical Logics and Approximate Reasoning, Beijing: Science Press, 2000, 207–274.

    Google Scholar 

  19. Ying, M. S., Automata theory based on quantum logic (I) (II), Int. J. Theor. Phys., 2000, 39(4): 981–991; 39(11): 2545–2557.

    Article  Google Scholar 

  20. Rosser, J. B., Turquette, A. R., Many-Valued Logics, Amsterdam: North-Holland, 1952.

    MATH  Google Scholar 

  21. Ying, M. S., Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets and Systems, 1993, 56: 337–373.

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Tsinghua University, 100084, Beijing, China

    Qiu Daowen

  2. Department of Computer Science, Zhongshan University, 510275, Guangzhou, China

    Qiu Daowen

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  1. Qiu Daowen
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Qiu, D. Automata theory based on complete residuated lattice-valued logic (II). Sci China Ser F 45, 442–452 (2002). https://doi.org/10.1360/02yf9038

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  • DOI: https://doi.org/10.1360/02yf9038

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