确定有限状态自动机最小化 (Chinese Wikipedia)

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Hopcroft (1971); Aho, Hopcroft & Ullman (1974) Hopcroft, John, An $n log n$ algorithm for minimizing states in a finite automaton, Theory of machines and computations (Proc. Internat. Sympos., Technion, Haifa, 1971), New York: Academic Press: 189–196, 1971, MR 0403320 . See also preliminary version, Technical Report STAN-CS-71-190 （页面存档备份，存于互联网档案馆）, Stanford University, Computer Science Department, January 1971. Aho, Alfred V.; Hopcroft, John E.; Ullman, Jeffrey D., 4.13 Partitioning, The Design and Analysis of Computer Algorithms, Addison-Wesley: 157–162, 1974 .
For instance, the language of binary strings whose nth symbol is a one requires only $n + 1$ states, but its reversal requires $2 n$ states. Leiss (1981) provides a ternary n-state DFA whose reversal requires $2 n$ states, the maximum possible. For additional examples and the observation of the connection between these examples and the worst-case analysis of Brzozowski's algorithm, see Câmpeanu et al. (2001). Leiss, Ernst, Succinct representation of regular languages by Boolean automata (PDF), Theoretical Computer Science, 1981, 13 (3): 323–330, MR 0603263, doi:10.1016/S0304-3975(81)80005-9 . Câmpeanu, Cezar; Culik, Karel, II; Salomaa, Kai; Yu, Sheng, State Complexity of Basic Operations on Finite Languages, 4th International Workshop on Automata Implementation (WIA '99), Lecture Notes in Computer Science 2214, Springer-Verlag: 60–70, 2001, doi:10.1007/3-540-45526-4_6 .

Berstel et al. (2010). Berstel, Jean; Boasson, Luc; Carton, Olivier; Fagnot, Isabelle, Minimization of Automata, Automata: from Mathematics to Applications, European Mathematical Society, 2010, arXiv:1010.5318

David (2012). David, Julien, Average complexity of Moore’s and Hopcroft’s algorithms, Theoretical Computer Science, 2012, 417: 50–65, doi:10.1016/j.tcs.2011.10.011 .
For instance, the language of binary strings whose nth symbol is a one requires only $n + 1$ states, but its reversal requires $2 n$ states. Leiss (1981) provides a ternary n-state DFA whose reversal requires $2 n$ states, the maximum possible. For additional examples and the observation of the connection between these examples and the worst-case analysis of Brzozowski's algorithm, see Câmpeanu et al. (2001). Leiss, Ernst, Succinct representation of regular languages by Boolean automata (PDF), Theoretical Computer Science, 1981, 13 (3): 323–330, MR 0603263, doi:10.1016/S0304-3975(81)80005-9 . Câmpeanu, Cezar; Culik, Karel, II; Salomaa, Kai; Yu, Sheng, State Complexity of Basic Operations on Finite Languages, 4th International Workshop on Automata Implementation (WIA '99), Lecture Notes in Computer Science 2214, Springer-Verlag: 60–70, 2001, doi:10.1007/3-540-45526-4_6 .
Kameda & Weiner (1970). Kameda, Tsunehiko; Weiner, Peter, On the state minimization of nondeterministic finite automata, IEEE Transactions on Computers, 1970, 100 (7), doi:10.1109/T-C.1970.222994 .

For instance, the language of binary strings whose nth symbol is a one requires only $n + 1$ states, but its reversal requires $2 n$ states. Leiss (1981) provides a ternary n-state DFA whose reversal requires $2 n$ states, the maximum possible. For additional examples and the observation of the connection between these examples and the worst-case analysis of Brzozowski's algorithm, see Câmpeanu et al. (2001). Leiss, Ernst, Succinct representation of regular languages by Boolean automata (PDF), Theoretical Computer Science, 1981, 13 (3): 323–330, MR 0603263, doi:10.1016/S0304-3975(81)80005-9 . Câmpeanu, Cezar; Culik, Karel, II; Salomaa, Kai; Yu, Sheng, State Complexity of Basic Operations on Finite Languages, 4th International Workshop on Automata Implementation (WIA '99), Lecture Notes in Computer Science 2214, Springer-Verlag: 60–70, 2001, doi:10.1007/3-540-45526-4_6 .

Hopcroft (1971); Aho, Hopcroft & Ullman (1974) Hopcroft, John, An $n log n$ algorithm for minimizing states in a finite automaton, Theory of machines and computations (Proc. Internat. Sympos., Technion, Haifa, 1971), New York: Academic Press: 189–196, 1971, MR 0403320 . See also preliminary version, Technical Report STAN-CS-71-190 （页面存档备份，存于互联网档案馆）, Stanford University, Computer Science Department, January 1971. Aho, Alfred V.; Hopcroft, John E.; Ullman, Jeffrey D., 4.13 Partitioning, The Design and Analysis of Computer Algorithms, Addison-Wesley: 157–162, 1974 .

Hopcroft (1971); Aho, Hopcroft & Ullman (1974) Hopcroft, John, An $n log n$ algorithm for minimizing states in a finite automaton, Theory of machines and computations (Proc. Internat. Sympos., Technion, Haifa, 1971), New York: Academic Press: 189–196, 1971, MR 0403320 . See also preliminary version, Technical Report STAN-CS-71-190 （页面存档备份，存于互联网档案馆）, Stanford University, Computer Science Department, January 1971. Aho, Alfred V.; Hopcroft, John E.; Ullman, Jeffrey D., 4.13 Partitioning, The Design and Analysis of Computer Algorithms, Addison-Wesley: 157–162, 1974 .