Minimization of states in automata theory based on finite lattice-ordered monoids

In this study, we consider a concept of complete L-fuzzy matrix, define complete lattice-valued finite automata (CLFAs) and study their properties. The definitions of statewise equivalence relations and automata equivalence relations of a CLFA are given, two algorithms are aimed at the minimization of states of a CLFA.

[1]  W. Wee.  On generalizations of adaptive algorithms and application of the fuzzy sets concept to pattern classification , 1967 .

[2]  N. C. Basak,et al.  On quotient machines of a fuzzy automaton and the minimal machine , 2002, Fuzzy Sets Syst..

[3]  Daowen Qiu,et al.  Supervisory control of fuzzy discrete event systems: a formal approach , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Witold Pedrycz,et al.  Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids , 2005, Fuzzy Sets Syst..

[5]  T. Stankowich.  Behavior , 2009, The Quarterly Review of Biology.

[6]  L. Peeva,et al.  Equivalence, Reduction and Minimization of Finite Automata over Semirings , 1991, Theor. Comput. Sci..

[7]  W. Pedrycz,et al.  Regular expressions with truth values in lattice-monoid and their languages , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[8]  K. Peeva.  Fuzzy automata and languages: theory and applications , 2004 .

[9]  Alexander Meduna.  Automata and languages - theory and applications , 2000 .

[10]  Zhihui Li,et al.  The relationships among several types of fuzzy automata , 2006, Inf. Sci..

[11]  Karvel K. Thornber,et al.  Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems , 1999, Proc. IEEE.

[12]  J. Mordeson,et al.  Fuzzy Discrete Structures , 2000 .

[13]  John N. Mordeson,et al.  Minimization of Fuzzy Finite Automata , 1999, Inf. Sci..

[14]  King-Sun Fu,et al.  A Formulation of Fuzzy Automata and Its Application as a Model of Learning Systems , 1969, IEEE Trans. Syst. Sci. Cybern..

[15]  Daowen Qiu.  Automata theory based on complete residuated lattice-valued logic , 2007, Science in China Series : Information Sciences.

[16]  Qiu Daowen,et al.  Automata theory based on complete residuated lattice-valued logic , 2001 .

[17]  Ketty Peeva,et al.  Finite 𝕃-fuzzy machines , 2004, Fuzzy Sets Syst..

[18]  Lotfi A. Zadeh,et al.  Note on fuzzy languages , 1969, Inf. Sci..

[19]  Wei Cheng,et al.  Minimization algorithm of fuzzy finite automata , 2004, Fuzzy Sets Syst..

[20]  Witold Pedrycz,et al.  Learning of Fuzzy Automata , 2001, Int. J. Comput. Intell. Appl..

[21]  Arun K. Majumdar,et al.  A formal power series approach to the construction of minimal fuzzy automata , 1991, Inf. Sci..

[22]  Witold Pedrycz,et al.  The equivalence between fuzzy Mealy and fuzzy Moore machines , 2006, Soft Comput..

[23]  Daowen Qiu,et al.  Characterizations of fuzzy finite automata , 2004, Fuzzy Sets Syst..

[24]  K. Peeva,et al.  Equivalence, reduction and minimization of finite fuzzy-automata , 1981 .

[25]  Madan M. Gupta,et al.  Fuzzy automata and decision processes , 1977 .

[26]  Karvel K. Thornber,et al.  Fuzzy finite-state automata can be deterministically encoded into recurrent neural networks , 1998, IEEE Trans. Fuzzy Syst..

[27]  K. Peeva.  Behaviour, reduction and minimization of finite :G6-automata , 1988 .