论文信息 - The State Complexities of Some Basic Operations on Regular Languages

The State Complexities of Some Basic Operations on Regular Languages

Abstract We consider the state complexities of some basic operations on regular languages. We show that the number of states that is sufficient and necessary in the worst case for a deterministic finite automaton (DFA) to accept the catenation of an m-state DFA language and an n-state DFA language is exactly m2n − 2n − 1, for m, n ⩾ 1. The result of 2n − 1 + 2n − 2 states is obtained for the star of an n-state DFA language, n1. State complexities for other basic operations and for regular languages over a one-letter alphabet are also studied.

[1] Sheng Yu,et al. Constructions for alternating finite automata , 1990, Int. J. Comput. Math..

[2] I. N. Sneddon,et al. Theory Of Automata , 1969 .

[3] A. R. Meyer,et al. Economy of Description by Automata, Grammars, and Formal Systems , 1971, SWAT.

[4] Jeffrey D. Ullman,et al. Introduction to Automata Theory, Languages and Computation , 1979 .

[5] Tao Jiang,et al. Minimal NFA Problems are Hard , 1991, SIAM J. Comput..

[6] B. Ravikumar,et al. Some applications of a technique of Sakoda and Sipser , 1990, SIGA.

[7] Oscar H. Ibarra,et al. Relating the Type of Ambiguity of Finite Automata to the Succinctness of Their Representation , 1989, SIAM J. Comput..

[8] Ernst L. Leiss,et al. Succint Representation of Regular Languages by Boolean Automata , 1981, Theor. Comput. Sci..