Conference paper

Editor list: Champarnaud, JM; Maurel, D

Publication year: 2003

Pages: 148-157

Journal: Lecture notes in computer science

Volume number: 2608

ISSN: 0302-9743

ISBN: 3-540-40391-4

Conference: 7th International Conference on Implementation and Application of Automata

Publisher: Springer

Title of series: LECTURE NOTES IN COMPUTER SCIENCE

Abstract: 
The state complexities of basic operations on nondeterministic finite automata (NFA) are investigated. In particular, we consider Boolean operations, catenation operations - concatenation, iteration, lambda-free iteration - and the reversal on NFAs that accept finite and infinite languages over arbitrary alphabets. Most of the shown bounds are tight in the exact number of states, i.e. the number is sufficient and necessary in the worst case. For the complementation. tight bounds in the order of magnitude are proved. It turns out that the state complexities of operations on NFAs and deterministic finite automata (DFA) are quite different. For example, the reversal and concatenation have exponential state complexity on DFAs but linear complexity on NFAs. Conversely, the complementation can be done with linear complexity on DFAs but needs exponentially many states on NFAs.

Harvard Citation style: Holzer, M. and Kutrib, M. (2003) State complexity of basic operations on nondeterministic finite automata, Lecture notes in computer science (Schriftenreihe), 2608, pp. 148-157

APA Citation style: Holzer, M., & Kutrib, M. (2003). State complexity of basic operations on nondeterministic finite automata. Lecture notes in computer science (Schriftenreihe). 2608, 148-157.