Fuzzy relation equations and reduction of fuzzy automata

Journal of Computer and System Sciences

Volumn 76, Issue 7, 2010, Pages 609-633

  Ćirić, Miroslav ^a   Stamenković, Aleksandar ^a   Ignjatović, Jelena ^a   Petković, Tatjana ^b  

^a UNIVERSITY OF NI   (Serbia)

^b NOKIA RESEARCH CENTER   (United States)

Author keywords

Alternate reduction; Complete residuated lattice; Factor fuzzy automaton; Fuzzy automaton; Fuzzy equivalence; Fuzzy relation equation; Right invariant fuzzy equivalence; State reduction

Indexed keywords

AUTOMATA THEORY; FUZZY RULES;

COMPLETE RESIDUATED LATTICES; FUZZY AUTOMATON; FUZZY EQUIVALENCE; FUZZY RELATION EQUATIONS; STATE REDUCTION;

ROBOTS;

EID: 77955428822     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2009.10.015     Document Type: Article

References (67)

1. N.C. Basak, and A. Gupta On quotient machines of a fuzzy automaton and the minimal machine Fuzzy Sets and Systems 125 2002 223 229
2. R. Blohlávek Fuzzy Relational Systems: Foundations and Principles 2002 Kluwer New York
3. R. Blohlávek, and V. Vychodil Fuzzy Equational Logic 2005 Springer Berlin, Heidelberg
4. J. Berstel, and Ch. Reutenauer Rational Series and Their Languages Monogr. Theoret. Comput. Sci. EATCS Ser. vol. 12 1988 Springer Berlin
5. P. Buchholz Bisimulation relations for weighted automata Theoret. Comput. Sci. 393 2008 109 123
6. S. Burris, H.P. Sankappanavar, and A. Course Universal Algebra 1981 Springer-Verlag New York
7. C.S. Calude, E. Calude, and B. Khoussainov Finite nondeterministic automata: Simulation and minimality Theoret. Comput. Sci. 242 2000 219 235
8. C. Câmpeanu, N. Sântean, and S. Yu Mergible states in large NFA Theoret. Comput. Sci. 330 2005 23 34
9. J.-M. Champarnaud, F. Coulon, Theoretical study and implementation of the canonical automaton, Technical Report AIA 2003.03, LIFAR, Université de Rouen, 2003
10. J.-M. Champarnaud, and F. Coulon NFA reduction algorithms by means of regular inequalities Z. Ésik, Z. Fülöp, DLT 2003 Lecture Notes in Comput. Sci. vol. 2710 2003 194 205
11. J.-M. Champarnaud, and F. Coulon NFA reduction algorithms by means of regular inequalities Theoret. Comput. Sci. 327 2004 241 253
12. J.-M. Champarnaud, and D. Ziadi New finite automaton constructions based on canonical derivatives S. Yu, A. Paun, CIAA 2000 Lecture Notes in Comput. Sci. vol. 2088 2001 Springer Berlin 94 104
13. J.-M. Champarnaud, and D. Ziadi Computing the equation automaton of a regular expression in O (s 2) space and time A. Amir, G. Landau, CPM 2001 Lecture Notes in Comput. Sci. vol. 2089 2001 Springer Berlin 157 168
14. W. Cheng, and Z. Mo Minimization algorithm of fuzzy finite automata Fuzzy Sets and Systems 141 2004 439 448
15. M. Ćirić, J. Ignjatović, and S. Bogdanović Fuzzy equivalence relations and their equivalence classes Fuzzy Sets and Systems 158 2007 1295 1313
16. M. Ćirić, J. Ignjatović, and S. Bogdanović Uniform fuzzy relations and fuzzy functions Fuzzy Sets and Systems 160 2009 1054 1081
17. M. Ćirić, A. Stamenković, J. Ignjatović, and T. Petković Factorization of fuzzy automata E. Csuhaj-Varju, Z. Ésik, FCT 2007 Lecture Notes in Comput. Sci. vol. 4639 2007 Springer Heidelberg 213 225
18. M. Demirci Topological properties of the class of generators of an indistinguishability operator Fuzzy Sets and Systems 143 2004 413 426
19. M. Demirci, and J. Recasens Fuzzy groups, fuzzy functions and fuzzy equivalence relations Fuzzy Sets and Systems 144 2004 441 458
20. A. Dovier, C. Piazza, and A. Policriti An efficient algorithm for computing bisimulation equivalence Theoret. Comput. Sci. 311 2004 221 256
21. S. Eilenberg Automata, Languages and Machines, vol. A 1974 Academic Press New York, London vol. B 1976
22. R. Gentilini, C. Piazza, and A. Policriti From bisimulation to simulation: Coarsest partition problems J. Automat. Reason. 31 2003 73 103
23. J. Högberg, A. Maletti, and J. May Backward and forward bisimulation minimisation of tree automata J. Holub, J. dárek, IAA07 Lecture Notes in Comput. Sci. vol. 4783 2007 Springer Heidelberg 109 121
24. J. Högberg, A. Maletti, and J. May Backward and forward bisimulation minimisation of tree automata Theoret. Comput. Sci. 410 2009 3539 3552
25. U. Höhle Commutative, residuated ℓ-monoids U. Höhle, E.P. Klement, Non-Classical Logics and Their Applications to Fuzzy Subsets 1995 Kluwer Academic Publishers Boston, Dordrecht 53 106
26. J. Ignjatović, M. Ćirić, and S. Bogdanović Determinization of fuzzy automata with membership values in complete residuated lattices Inform. Sci. 178 2008 164 180
27. J. Ignjatović, M. Ćirić, S. Bogdanović, T. Petković, Myhill-Nerode type theory for fuzzy languages and automata, Fuzzy Sets and Systems (2009), doi:10.1016/j.fss.2009.06.007, in press
28. L. Ilie, and S. Yu Constructing NFAs by optimal use of positions in regular expressions A. Apostolico, M. Takeda, CPM 2002 Lecture Notes in Comput. Sci. vol. 2373 2002 Springer Berlin 279 288
29. L. Ilie, and S. Yu Algorithms for computing small NFAs K. Diks, MFCS 2002 Lecture Notes in Comput. Sci. vol. 2420 2002 328 340
30. L. Ilie, and S. Yu Reducing NFAs by invariant equivalences Theoret. Comput. Sci. 306 2003 373 390
31. L. Ilie, and S. Yu Follow automata Inform. and Comput. 186 2003 140 162
32. L. Ilie, G. Navarro, and S. Yu On NFA reductions J. Karhumäki, Theory is Forever Lecture Notes in Comput. Sci. vol. 3113 2004 112 124
33. L. Ilie, R. Solis-Oba, and S. Yu Reducing the size of NFAs by using equivalences and preorders A. Apostolico, M. Crochemore, K. Park, CPM 2005 Lecture Notes in Comput. Sci. vol. 3537 2005 310 321
34. T. Jiang, and B. Ravikumar Minimal NFA problems are hard SIAM J. Comput. 22 6 1993 1117 1141
35. T. Kameda, and P. Weiner On the state minimization of nondeterministic finite automata IEEE Trans. Comput. C-19 7 1970 617 627
36. P.C. Kannellakis, and S.A. Smolka CCS expressions, finite state processes, and three problems of equivalence Inform. and Comput. 86 1990 43 68
37. F. Klawonn Fuzzy points, fuzzy relations and fuzzy functions V. Novâk, I. Perfilieva, Discovering World with Fuzzy Logic 2000 Physica-Verlag Heidelberg 431 453
38. F. Klawonn, and J.L. Castro Similarity in fuzzy reasoning Mathware Soft Comput. 2 1995 197 228
39. F. Klawonn, and R. Kruse Equality relations as a basis for fuzzy control Fuzzy Sets and Systems 54 1993 147 156
40. W. Kuich, and A. Salomaa Semirings, Automata, Languages Monogr. Theoret. Comput. Sci. EATCS Ser. vol. 5 1986 Springer-Verlag
41. H. Lei, and Y.M. Li Minimization of states in automata theory based on finite lattice-ordered monoids Inform. Sci. 177 2007 1413 1421
42. Y.M. Li, and W. Pedrycz Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids Fuzzy Sets and Systems 156 2005 68 92
43. N. Lynch, and F. Vaandrager Forward and backward simulations: Part I. Untimed systems Inform. and Comput. 121 1995 214 233
44. D.S. Malik, J.N. Mordeson, and M.K. Sen Minimization of fuzzy finite automata Inform. Sci. 113 1999 323 330
45. B.F. Melnikov A new algorithm of the state-minimization for the nondeterministic finite automata Korean J. Comput. Appl. Math. 6 2 1999 277 290
46. B.F. Melnikov Once more about the state-minimization of the nondeterministic finite automata Korean J. Comput. Appl. Math. 7 3 2000 655 662
47. R. Milner A calculus of communicating systems G. Goos, J. Hartmanis, Lecture Notes in Comput. Sci. vol. 92 1980 Springer
48. R. Milner Communication and Concurrency 1989 Prentice Hall International
49. R. Milner Communicating and Mobile Systems: The π-Calculus 1999 Cambridge University Press Cambridge
50. J.N. Mordeson, and D.S. Malik Fuzzy Automata and Languages: Theory and Applications 2002 Chapman & Hall/CRC Boca Raton, London
51. R. Paige, and R.E. Tarjan Three partition refinement algorithms SIAM J. Comput. 16 6 1987 973 989
52. D. Park Concurrency and automata on infinite sequences P. Deussen, Proc. 5th GI Conf. Lecture Notes in Comput. Sci. vol. 104 1981 Springer-Verlag Karlsruhe, Germany 167 183
53. T. Petković Congruences and homomorphisms of fuzzy automata Fuzzy Sets and Systems 157 2006 444 458
54. D.W. Qiu Automata theory based on completed residuated lattice-valued logic (I) Sci. China Ser. F 44 6 2001 419 429
55. D.W. Qiu Automata theory based on completed residuated lattice-valued logic (II) Sci. China Ser. F 45 6 2002 442 452
56. D.W. Qiu Pumping lemma in automata theory based on complete residuated lattice-valued logic: A note Fuzzy Sets and Systems 157 2006 2128 2138
57. F. Ranzato, and F. Tapparo Generalizing the Paige-Tarjan algorithm by abstract interpretation Inform. and Comput. 206 2008 620 651
58. M. Roggenbach, and M. Majster-Cederbaum Towards a unified view of bisimulation: A comparative study Theoret. Comput. Sci. 238 2000 81 130
59. A. Salomaa, and M. Soittola Automata-Theoretic Aspects of Formal Power Series 1978 Springer-Verlag New York, Heidelberg, Berlin
60. D. Sangiorgi, On the origins of bisimulation, coinduction, and fixed points, Technical Report UBLCS-2007-24, Department of Computer Science, University of Bologna, 2007
61. H. Sengoku, Minimization of nondeterministic finite automata, Master thesis, Kyoto University, 1992
62. L. Valverde On the structure of F-indistinguishability operators Fuzzy Sets and Systems 17 1985 313 328
63. H.G. Xing, and D.W. Qiu Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic Fuzzy Sets and Systems 160 2009 1141 1151
64. H.G. Xing, and D.W. Qiu Automata theory based on complete residuated lattice-valued logic: A categorical approach Fuzzy Sets and Systems 160 2009 2416 2428
65. H.G. Xing, D.W. Qiu, and F.C. Liu Automata theory based on complete residuated lattice-valued logic: Pushdown automata Fuzzy Sets and Systems 160 2009 1125 1140
66. H.G. Xing, D.W. Qiu, F.C. Liu, and Z.J. Fan Equivalence in automata theory based on complete residuated lattice-valued logic Fuzzy Sets and Systems 158 2007 1407 1422
67. S. Yu Regular languages G. Rozenberg, A. Salomaa, Handbook of Formal Languages, vol. 1 1997 Springer-Verlag Berlin, Heidelberg 41 110