Lattice Minimal Automata and Lattice Reduced Automata

  • Yang Wang
  • Zhi-wen Mo
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 54)


We apply lattice ordered monoids in the study of lattice finite automata, and obtain some results similar to the ones of fuzzy finite automata. In this paper, the concepts of lattice minimal automata and lattice reduced automata are put forward, and the relationship of them associated with an L-language is discussed. Moreover, the L-fuzzy equivalence relation on states is defined, and an algorithm to minimize the lattice finite automata is presented based on clustering states.


Lattice minimal automata Lattice reduced automata L-regular language L-fuzzy equivalence Clustering 


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  1. 1.
    Zadeh, L.: A Fuzzy sets. Information Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Wee, W.G.: On generalization of adaptive algorithm and application of the fuzzy sets concept to pattern classification. Ph. D. Thesis, Purdue University (1967)Google Scholar
  3. 3.
    Qiu, D.W.: Automata theory based on completed residuated lattice-valued logic(I). Science in China, Series F44 6, 419–429 (2001)Google Scholar
  4. 4.
    Qiu, D.W.: Automata theory based on completed residuated lattice-valued logic(II). Science in China, Series F45 6, 442–452 (2002)Google Scholar
  5. 5.
    Li, Y.M., Pedrycz, W.: Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids. Fuzzy Sets and Systems 156, 68–92 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Cheng, W., Mo, Z.W.: Minimization algorithm of fuzzy finite automata. Fuzzy Sets and Systems 141, 439–448 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Mo, Z.W., Peng, J.Y.: Fuzzy minimal automaton and reduced fuzzy automaton. Journal of Sichuan Normal University, Series 25(6), 585–587 (2002)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Horng, M.S.: State minimization of fuzzy automaton, pp. 1946–1949. IEEE, Los Alamitos (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yang Wang
    • 1
  • Zhi-wen Mo
    • 1
  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityP.R. China

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