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

Information Sciences

Volumn 177, Issue 6, 2007, Pages 1413-1421

  Lei, Hongxuan ^a,b   Li, Yongming ^a  

^a SHAANXI NORMAL UNIVERSITY   (China)

^b NEIJIANG NORMAL UNIVERSITY   (China)

Author keywords

Equivalence; Fuzzy finite automata; L Fuzzy matrix; Lattice ordered monoid; Minimization algorithm

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; EQUIVALENCE CLASSES; FUZZY SETS; MATRIX ALGEBRA; OPTIMIZATION;

COMPLETE LATTICE VALUED FINITE AUTOMATA (CLFA); FUZZY FINITE AUTOMATA; L FUZZY MATRIX; LATTICE ORDERED MONOIDS; MINIMIZATION ALGORITHMS;

FINITE AUTOMATA;

EID: 33845920084     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2006.07.015     Document Type: Article

References (26)

1. Basak N.C., and Gupta A. On quotient machines of a fuzzy automata and the minimal machine. Fuzzy Sets and Systems 125 (2002) 223-229
2. Cheng W., and Mo Z.W. Minimization algorithm of fuzzy finite automata. Fuzzy Sets and Systems 141 (2004) 439-448
3. Gupta M.M., Saridis G.N., and Gaines B.R. Fuzzy Automata and Decision Processes (1977), North-Holland, New York pp. 111-175
4. Lee E.T., and Zadeh L.A. Note on fuzzy languages. Information Sciences 1 (1969) 421-434
5. Li Y.M. Finite automata with truth values in lattice-monoid and their languages. Journal of Shaanxi Normal University (Natural Science Edition) 4 (2003) 1-6
6. Y.M. Li, W. Pedrycz, Regular expressions with truth values in lattice-moniod and their languages, in: 2004 Annual Meeting of The North American Fuzzy Information Processing Society, 2004 IEEE ISBN 0-7803-8377-X IEEE Cat. No. 04TH8736C, Banff, Alberta, Canada, June 27-30, 2004, pp. 572-577.
7. Y.M. Li, Lattice-valued finite automata and their languages, in: 8th World Multiconference on Systematics, Cybernetics and Informatics (SCI2004), July 18-21, 2004, Orlando, FL, USA, pp. 213-218.
8. Li Y.M., and Pedrycz W. Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoid. Fuzzy Sets and Systems 156 (2005) 68-92
9. Li Y.M., and Pedrycz W. The equivalence between fuzzy mealy and fuzzy moore machines. Soft Computing 10 (2006) 953-959
10. Li Z.H., Li P., and Li Y.M. The relationships among several types of fuzzy finite automata. Information Sciences 176 (2006) 2208-2226
11. Malik D.S., Mordeson J.N., and Sen M.K. Minimization of fuzzy finite automata. Information Sciences 113 (1999) 323-330
12. Malik D.S., and Mordeson J.N. Fuzzy Discrete Structures (2000), Physica-Verlag, New York
13. Mordeson J.N., and Malik D.S. Fuzzy Automata and Languages: Theory and Applications (2002), Chapman & Hall/CRC, Boca Raton, London
14. Omlin C.W., Thornber K.K., and Giles C.L. Fuzzy finite-state automata can be deterministically encoded in recurrent neural networks. IEEE Transactions on Fuzzy Systems 5 (1998) 76-89
15. Giles C.L., Omlin C.W., and Thornber K.K. Equivalence in knowledge representation: automata, recurrent neural networks, and dynamical fuzzy systems. Proceedings of IEEE 87 (1999) 1623-1640
16. Pedrycz W., and Gacek A. Learning of fuzzy automata. International Journal of Computational Intelligence and Applications 1 (2001) 19-33
17. Peeva K. Behavior, reduction and minimization of finite L-automata. Fuzzy Sets and Systems 28 (1988) 171-181
18. Peeva K. Equivalence, reduction and minimization of finite automata over semirings. Theoretical Computer Science 88 (1991) 269-285
19. Peeva K. Finite L-fuzzy machines. Fuzzy Sets and Systems 141 (2004) 415-437
20. Qiu D.W. Automata theory based on complete residuated lattice-valued logic. Science in China (Series F) 44 (2001) 419-429
21. Qiu D.W. Characterizations of fuzzy finite automata. Fuzzy Sets and Systems 141 (2004) 391-414
22. Qiu D. Supervisory control of fuzzy discrete event systems: a formal approach. IEEE Transactions on Systems, Man and Cybernetics-Part B 35 (2005) 72-88
23. Ray A.K., Chatterjee B., and Majumdar A.K. A formal power series approach to the construction of minimal fuzzy automata. Information Sciences 55 (1991) 189-207
24. Topencharov V., and Peeva K. Equivalence, reduction and minimization of finite fuzzy automata. Journal of Mathematical Analysis and Applications 84 (1981) 270-281
25. W.G. Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification, Ph.D. Thesis, Purdue University, June 1967.
26. Wee W.G., and Fu K.S. A formulation of fuzzy automata and its application as a model of learning systems. IEEE Transactions on Systems, Man and Cybernetics 5 (1969) 215-223