Myhill-Nerode type theory for fuzzy languages and automata

Fuzzy Sets and Systems

Volumn 161, Issue 9, 2010, Pages 1288-1324

  Ignjatović, Jelena ^a   Ćirić, Miroslav ^a   Bogdanović, Stojan ^a   Petković, Tatjana ^b  

^a UNIVERSITY OF NI   (Serbia)

^b NOKIA RESEARCH CENTER   (United States)

Author keywords

Derivative automaton; Deterministic automaton; Fuzzy automaton; Fuzzy language; Minimal automaton; Myhill's automaton; Myhill Nerode theorem; Nerode's automaton; Syntactic monoid

Indexed keywords

DETERMINISTIC AUTOMATA; FUZZY AUTOMATON; FUZZY LANGUAGE; MINIMAL AUTOMATON; MYHILL-NERODE THEOREM; SYNTACTIC MONOID;

FINITE AUTOMATA; FORMAL LANGUAGES; FUZZY SET THEORY; FUZZY SYSTEMS; LINGUISTICS; QUERY LANGUAGES; SYNTACTICS; TRANSLATION (LANGUAGES);

ROBOTS;

EID: 77949541128     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2009.06.007     Document Type: Article

References (79)

1. Asveld P.R.J. Algebraic aspects of families of fuzzy languages. Theoretical Computer Science 293 (2003) 417-445
2. Basak N.C., and Gupta A. On quotient machines of a fuzzy automaton and the minimal machine. Fuzzy Sets and Systems 125 (2002) 223-229
3. Bělohlávek R. Fuzzy Relational Systems: Foundations and Principles (2002), Kluwer, New York
4. Bělohlávek R. Determinism and fuzzy automata. Information Sciences 143 (2002) 205-209
5. Bělohlávek R., and Vychodil V. Fuzzy Equational Logic (2005), Springer, Berlin, Heidelberg
6. B. Borchardt, The Myhill-Nerode theorem for recognizable tree series, in: Z. Ésik, Z. Fülöp (Eds.), DLT 2003, Lecture Notes in Computer Science, Vol. 2710, Springer, Heidelberg, 2003, pp. 146-158.
7. Borchardt B., Maletti A., Šešelja B., Tepavčević A., and Vogler H. Cut sets as recognizable tree languages. Fuzzy Sets and Systems 157 (2006) 1560-1571
8. Bozapalidis S., and Louscou-Bozapalidou O. On the recognizability of fuzzy languages I. Fuzzy Sets and Systems 157 (2006) 2394-2402
9. Bozapalidis S., and Louscou-Bozapalidou O. On the recognizability of fuzzy languages II. Fuzzy Sets and Systems 159 (2008) 107-113
10. Burris S., and Sankappanavar H.P. A Course in Universal Algebra (1981), Springer, New York
11. Cheng W., and Mo Z. Minimization algorithm of fuzzy finite automata. Fuzzy Sets and Systems 141 (2004) 439-448
12. Ćirić M., Ignjatović J., and Bogdanović S. Fuzzy equivalence relations and their equivalence classes. Fuzzy Sets and Systems 158 (2007) 1295-1313
13. M. Ćirić, A. Stamenković, J. Ignjatović, T. Petković, Factorization of fuzzy automata, in: Csuhaj-Varju, E., Ésik, Z. (Eds.), FCT 2007, Lecture Notes in Computer Science, Vol. 4639, Springer, Heidelberg, 2007, pp. 213-225.
14. M. Ćirić, A. Stamenković, J. Ignjatović, T. Petković, Fuzzy relation equations and reduction of fuzzy automata, submitted for publication.
15. Davey B.A., and Priestley H.A. Introduction to Lattices and Order (1990), Cambridge University Press, Cambridge
16. De Luca A., and Varricchio S. Finiteness and Regularity in Semigroups and Formal Languages (1999), Springer, Berlin, Heidelberg
17. Demirci M. Topological properties of the class of generators of an indistinguishability operator. Fuzzy Sets and Systems 143 (2004) 413-426
18. Demirci M., and Recasens J. Fuzzy groups, fuzzy functions and fuzzy equivalence relations. Fuzzy Sets and Systems 144 (2004) 441-458
19. Droste M., and Gastin P. Weighted automata and weighted logics. Theoretical Computer Science 380 (2007) 69-86
20. S. Eilenberg, Automata, Languages and Machines, Vol. A, 1974, Vol. B, 1976, Academic Press, New York, London.
21. J. Eisner, Simpler and more general minimization for weighted finite-state automata, in: HLT-NAACL, 2003.
22. C.C. Elgot, J.D. Rutledge, Operations on finite automata, in: Proc. AIEE Second Annu. Symp. on Switching Theory and Logical Design, Detroit, MI, 1961.
23. Guo X. Grammar theory based on lattice-ordered monoid. Fuzzy Sets and Systems 160 (2009) 1152-1161
24. Höhle U. Commutative, residuated ℓ-monoids. In: Höhle U., and Klement E.P. (Eds). Non-Classical Logics and Their Applications to Fuzzy Subsets (1995), Kluwer Academic Publishers, Boston, Dordrecht 53-106
25. Ignjatović J., Ćirić M., and Bogdanović S. Determinization of fuzzy automata with membership values in complete residuated lattices. Information Sciences 178 (2008) 164-180
26. Klawonn F. Fuzzy points, fuzzy relations and fuzzy functions. In: Novâk V., and Perfilieva I. (Eds). Discovering World with Fuzzy Logic (2000), Physica-Verlag, Heidelberg 431-453
27. Klawonn F., and Castro J.L. Similarity in fuzzy reasoning. Mathware Soft Computing 2 (1995) 197-228
28. Klawonn F., and Kruse R. Equality relations as a basis for fuzzy control. Fuzzy Sets and Systems 54 (1993) 147-156
29. Kozen D. On the Myhill-Nerode theorem for trees. Bulletin of the EATCS 47 (1992) 170-173
30. Lawson M.V. Finite Automata (2004), Chapman & Hall, CRC, Boca Raton, London
31. Lee E.T., and Zadeh L.A. Note on fuzzy languages. Information Sciences 1 (1969) 421-434
32. Lei H., and Li Y.M. Minimization of states in automata theory based on finite lattice-ordered monoids. Information Sciences 177 (2007) 1413-1421
33. Li P., and Li Y.M. Algebraic properties of LA-languages. Information Sciences 176 (2006) 3232-3255
34. Li Y.M. A categorical approach to lattice-valued fuzzy automata. Fuzzy Sets and Systems 157 (2006) 855-864
35. Y.M. Li, Finite automata based on quantum logic and their determinization, CoRR abs/0712.4341, 2007.
36. Li Y.M. Approximation and robustness of fuzzy finite automata. International Journal of Approximate Reasoning 47 (2008) 247-257
37. Li Y.M., and Pedrycz W. Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids. Fuzzy Sets and Systems 156 (2005) 68-92
38. Li Y.M., and Pedrycz W. The equivalence between fuzzy Mealy and fuzzy Moore machines. Soft Computing 10 (2006) 953-959
39. Li Y.M., and Pedrycz W. Minimization of lattice finite automata and its application to the decomposition of lattice languages. Fuzzy Sets and Systems 158 (2007) 1423-1436
40. Li Z., Li P., and Li Y.M. The relationships among several types of fuzzy automata. Information Sciences 176 (2006) 2208-2226
41. Liang C.J., and Li Y.M. Algebraic properties on the cuts of lattice-valued regular languages. Soft Computing 12 (2008) 1049-1057
42. A. Maletti, Myhill-Nerode theorem for recognizable tree series revisited, in: E.S. Laber, et al. (Eds.), LATIN 2008, Lecture Notes in Computer Science, Vol. 4957, Springer, Heidelberg, 2008, pp. 106-120.
43. Malik D.S., Mordeson J.N., and Sen M.K. On fuzzy regular languages. Information Sciences 88 (1996) 263-273
44. Malik D.S., Mordeson J.N., and Sen M.K. Products of fuzzy finite state machines. Fuzzy Sets and Systems 92 (1997) 95-102
45. Malik D.S., Mordeson J.N., and Sen M.K. Minimization of fuzzy finite automata. Information Sciences 113 (1999) 323-330
46. Mordeson J.N., and Malik D.S. Fuzzy Automata and Languages: Theory and Applications (2002), Chapman & Hall, CRC, Boca Raton, London
47. Mordeson J.N., Malik D.S., and Kuroki N. Fuzzy Semigroups (2003), Springer, Berlin
48. J. Myhill, Finite automata and the representation of events, in: WADD TR-57-624, Wright Patterson AFB, Ohio, 1957, pp. 112-137.
49. A. Nerode, Linear automata transformation, in: Proc. American Mathematical Society, Vol. 9, 1958, pp. 541-544.
50. T. Petković, Varieties of fuzzy languages, in: Proc. 1st Internat. Conf. on Algebraic Informatics, Aristotle University of Thessaloniki, Thessaloniki, 2005, pp. 197-205.
51. Petković T. Congruences and homomorphisms of fuzzy automata. Fuzzy Sets and Systems 157 (2006) 444-458
52. Petković T., Ćirić M., and Bogdanović S. Unary algebras, semigroups and congruences on free semigroups. Theoretical Computer Science 324 1 (2004) 87-105
53. Petković T., Ćirić M., and Bogdanović S. On correspondences between unary algebras, automata, semigroups and congruences. Algebra Colloquium 13 3 (2006) 495-506
54. J.E. Pin, Syntactic semigroups, in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, Vol. 1, Springer, Berlin, Heidelberg, 1997, pp. 679-746.
55. Qiu D.W. Automata theory based on completed residuated lattice-valued logic (I). Science in China, Series F 44 6 (2001) 419-429
56. Qiu D.W. Automata theory based on completed residuated lattice-valued logic (II). Science in China, Series F 45 6 (2002) 442-452
57. Qiu D.W. Automata theory based on quantum logic: some characterizations. Information and Computation 190 (2004) 179-195
58. Qiu D.W. Pumping lemma in automata theory based on complete residuated lattice-valued logic: a note. Fuzzy Sets and Systems 157 (2006) 2128-2138
59. Qiu D.W. Automata theory based on quantum logic: reversibilities and pushdown automata. Theoretical Computer Science 386 (2007) 38-56
60. Rabin M.O., and Scott D. Finite automata and their decision problems. IBM Journal of Research and Development 3 (1959) 114-125
61. Raney G.N. Sequential functions. Journal of the ACM 5 (1958) 177-180
62. Šešelja B., Tepavčević A., and Vogler H. A note on cut-worthiness of recognizable tree series. Fuzzy Sets and Systems 159 (2008) 3087-3090
63. Santos E.S. Maximin automata. Information and Control 12 (1968) 367-377
64. Santos E.S. On reduction of max-min machines. Journal of Mathematical Analysis and Applications 37 (1972) 677-686
65. Santos E.S. Fuzzy automata and languages. Information Sciences 10 (1976) 193-197
66. Shen J. Fuzzy language on free monoid. Information Sciences 88 (1996) 149-168
67. Sheng L., and Li Y.M. Regular grammars with truth values in lattice-ordered monoid and their languages. Soft Computing 10 (2006) 79-86
68. M. Steinby, Classifying regular languages by their syntactic algebras, in: Results and Trends in Theoretical Computer Science, Graz, 1994, Lecture Notes in Computer Science, Vol. 812, Springer, Berlin, 1994, pp. 396-409.
69. Walker C.L., and Walker E.A. The algebra of fuzzy truth values. Fuzzy Sets and Systems 149 (2005) 309-347
70. 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.
71. 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
72. Xing H.G., and Qiu D.W. Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic. Fuzzy Sets and Systems 160 (2009) 1141-1151
73. Xing H.G., and Qiu D.W. Automata theory based on complete residuated lattice-valued logic: a categorical approach. Fuzzy Sets and Systems 160 (2009) 2416-2428
74. Xing H.G., Qiu D.W., and Liu F.C. Automata theory based on complete residuated lattice-valued logic: pushdown automata. Fuzzy Sets and Systems 160 (2009) 1125-1140
75. Xing H.G., Qiu D.W., Liu F.C., and Fan Z.J. Equivalence in automata theory based on complete residuated lattice-valued logic. Fuzzy Sets and Systems 158 (2007) 1407-1422
76. Ying M.S. Automata theory based on quantum logic (I). International Journal of Theoretical Physics 39 (2000) 985-995
77. Ying M.S. Automata theory based on quantum logic (II). International Journal of Theoretical Physics 39 (2000) 2545-2557
78. Ying M.S. A theory of computation based on quantum logic (I). Theoretical Computer Science 344 (2005) 134-207
79. S. Yu, Regular languages, in: G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, Vol. 1, Springer, Berlin, Heidelberg, 1997, pp. 41-110.