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An Improved Proof of the Closure Under Homomorphic Inverse of FCFL Valued in Lattice-Ordered Monoids

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Theoretical Computer Science (NCTCS 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1069))

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Abstract

We study fuzzy context-free grammars (FCFG), fuzzy context-free languages (FCFL) and fuzzy pushdown automata (FPDA) valued in lattice-ordered monoids. Inspired by the ideas of crisp cases, we get similar results, but some of them depend on commutative law. Particularly, we give two proofs of the closure under homomorphic inverse of FCFL when lattice-ordered monoids are commutative. Comparing with the classical method, we show that the improved proof is more efficient.

Supported by the National Natural Science Foundation of China under Grant 11301321, Grant 61673250, Grant 61672023.

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References

  1. Alasdair, U.: Balbes Raymond and Dwinger Philip. Distributive lattices. University of Missouri Press, Columbia 1974, xiii + 294 pp. J. Symb. Logic 42, 294–588 (1997)

    Google Scholar 

  2. Asveld, P.R.J.: Algebraic aspects of families of fuzzy languages. Theoret. Comput. Sci. 293(2), 417–445 (2003)

    Article  MathSciNet  Google Scholar 

  3. Asveld, P.R.J.: Fuzzy context-free languages part 1: generalized fuzzy context-free grammars. Theoret. Comput. Sci. 347(1), 167–190 (2005)

    Article  MathSciNet  Google Scholar 

  4. Depalma, G.F., Yau, S.S.: Fractionally fuzzy grammars with application to pattern recognition. In: Fuzzy Sets & Their Applications to Cognitive & Decision Processes, pp. 329–351 (1975)

    Google Scholar 

  5. Dilworth, R.P., Birkhoff, G.: Lattice theory. Bull. Am. Math. Soc. 56, 204–206 (1950)

    Article  Google Scholar 

  6. Gerla, G.: Fuzzy grammars and recursively enumerable fuzzy languages. Inf. Sci. 60(1C2), 137–143 (1992)

    Article  MathSciNet  Google Scholar 

  7. Guo, X.: Grammar theory based on lattice-ordered monoid. Fuzzy Sets Syst. 160(8), 1152–1161 (2009)

    Article  MathSciNet  Google Scholar 

  8. Guo, X.: A comment on automata theory based on complete residuated lattice-valued logic: pushdown automata (2012)

    Article  MathSciNet  Google Scholar 

  9. Jiang, Z., Jiang, S.: Formal languages and automata. Tsinghua University Press (2003)

    Google Scholar 

  10. Jin, J., Li, Q.: Fuzzy grammar theory based on lattices. Soft Comput. 16(8), 1415–1426 (2012)

    Article  Google Scholar 

  11. Kim, H.H., Mizumoto, M., Toyoda, J., Tanaka, K.: L -fuzzy grammars. Inf. Sci. 8(2), 123–140 (1975)

    Article  MathSciNet  Google Scholar 

  12. Lan, S.: A machine accepted fuzzy context-free languages and fuzzy pushdown automata. BUSEFAL 49(6), 67–72 (1992)

    Google Scholar 

  13. Lee, E.T., Zadeh, L.A.: Note on fuzzy languages. Inf. Sci. 1(4), 421–434 (1969)

    Article  MathSciNet  Google Scholar 

  14. Lee, E.T., Zadeh, L.A.: Fuzzy languages and their acceptance by automata. In: Fourth Princeton Conference Information Science and System, no. 2, pp. 399–410 (1970)

    Google Scholar 

  15. Li, P., Li, Y.M.: Algebraic properties of la-languages. Inf. Sci. 176(21), 3232–3255 (2006)

    Article  MathSciNet  Google Scholar 

  16. Li, Y., Li, P.: Fuzzy computing theory. Science Press (2016)

    Google Scholar 

  17. Li, Y., Pedrycz, W.: Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids. Fuzzy Sets Syst. 156(25), 68–92 (2005)

    Article  MathSciNet  Google Scholar 

  18. Li, Z., Li, P., Li, Y.: The relationships among several types of fuzzy automata. Inf. Sci. 176(15), 2208–2226 (2006)

    Article  MathSciNet  Google Scholar 

  19. Omlin, C.W., Giles, C.L.: Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems. Proc. IEEE 87(9), 1623–1640 (1999)

    Article  Google Scholar 

  20. Pan, H., Song, F., Cao, Y., Qian, J.: Fuzzy pushdown termination games. IEEE Trans. Fuzzy Syst. 27(15), 760–774 (2019)

    Article  Google Scholar 

  21. Qiu, D.: Automata theory based on complete residuated latticed-valued logic(i). Sci. China (Series E) 33(10), 137–146 (2003)

    Google Scholar 

  22. Santos, E.: Fuzzy automata and languages. Inf. Sci. 10(3), 193–197 (1976)

    Article  Google Scholar 

  23. Santos, E.S.: Maximin automata. Inf. Control 13(4), 363–377 (1968)

    Article  MathSciNet  Google Scholar 

  24. Schtzenberger, M.: On context-free languages and push-down automata. Inf. Control 6(3), 246–264 (1963)

    Article  MathSciNet  Google Scholar 

  25. Senay, H.: Fuzzy command grammars for intelligent interface design. IEEE Trans. Syst. Man Cybern. 22(5), 1124–1131 (1992)

    Article  Google Scholar 

  26. Steimann, F., Adlassnig, K.P.: Clinical monitoring with fuzzy automata. Fuzzy Sets Syst. 61(1), 37–42 (1994)

    Article  MathSciNet  Google Scholar 

  27. Wang, H., Qiu, D.: Computing with words via turing machines: a formal approach. IEEE Trans. Fuzzy Syst. 11(6), 742–753 (2003)

    Article  Google Scholar 

  28. Xing, H.: Fuzzy pushdown automata. Fuzzy Sets Syst. 158(13), 1437–1449 (2007)

    Article  MathSciNet  Google Scholar 

  29. Xing, H., Qiu, D.: Automata theory based on complete residuated lattice-valued logic: a categorical approach. Fuzzy Sets Syst. 160(16), 2416–2428 (2009)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Haihui Wang, Luyao Zhao & Ping Li

Authors
  1. Haihui Wang
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  2. Luyao Zhao
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  3. Ping Li
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Corresponding author

Correspondence to Ping Li .

Editor information

Editors and Affiliations

  1. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  2. Huazhong University of Science and Technology, Wuhan, China

    Kun He

  3. Lanzhou University, Lanzhou, China

    Xiaoyun Chen

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Wang, H., Zhao, L., Li, P. (2019). An Improved Proof of the Closure Under Homomorphic Inverse of FCFL Valued in Lattice-Ordered Monoids. In: Sun, X., He, K., Chen, X. (eds) Theoretical Computer Science. NCTCS 2019. Communications in Computer and Information Science, vol 1069. Springer, Singapore. https://doi.org/10.1007/978-981-15-0105-0_5

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  • DOI: https://doi.org/10.1007/978-981-15-0105-0_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-0104-3

  • Online ISBN: 978-981-15-0105-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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