How to use sorting procedures to minimize DFA
In this paper we introduce a new idea, which can be used in minimization of a deterministic finite automaton. Namely, we associate names with states of an automaton and we sort them. We give a new algorithm, its correctness proof, and its proof of execution time bound. This algorithm has time complexity O(n2 log n) and can be considered as a direct improvement of Wood's algorithm  which has time complexity O(n3), where n is the number of states. Wood's algorithm checks if pairs of states are distinguishable. It is improved by making better use of transitivity. Similarly some other algorithms which check if pairs of states are distinguishable can be improved using sorting procedures.
Unable to display preview. Download preview PDF.
- 1.J. A. Brzozowski, H. Jürgensen: A model for Sequential Machine Testing and Diagnosis, Journal of Electronic Testing: Theory and Applications 3 (1992), 219–234.Google Scholar
- 2.J. E. Hopcroft: An n log n algorithm for minimizing the states in a finite automaton, in: Z. Kohavi, ed., The Theory of Machines and Computations, Academic Press, New York, 1971, 189–196.Google Scholar
- 3.J. E. Hopcroft, J. D. Ullman: Introduction to Automata Theory, Languages and Computation, Addison-Wesley, New Jersey, March 1979.Google Scholar
- 4.B. Schubert: How to Use Sorting Procedures to Minimize DFA, MSc Thesis, Department of Computer Science, University of Western Ontario, in preparation.Google Scholar
- 5.B. W. Watson: Taxonomies and Toolkits of Regular Language Algorithms, Eindhoven University of Technology, The Netherlands, 1995.Google Scholar
- 6.D. Wood: Theory of Computation, John Wiley & Sons, New York, 1987.Google Scholar