FA Minimisation Heuristics for a Class of Finite Languages
In this paper, we deal with minimization of finite automata associated with finite languages all the words have the same length. This problem arises in the context of Constraint Satisfaction Problems, widely used in AI. We first give some complexity results which are based on the strong relationship with covering problems of bipartite graphs. We then use these coverings as a basic tool for the definition of minimization heuristics, and describe some experimental results.
KeywordsBipartite Graph Constraint Satisfaction Problem Finite Automaton Reduction Operation State Automaton
Unable to display preview. Download preview PDF.
- [DWW98]J. Daciuk, W. Watson, and B.W. Watson. Incremental construction of minimal acyclic finite state automata and transducers. In Finite State Methods in Natural Language Processing, Ankara, Turkey, 1998.Google Scholar
- [FH93]P.C. Fishburn and P.L. Hammer. Bipartite dimensions and bipartite degrees of graphs. Technical Report 76, DIMACS, June 1993. available at http://dimacs.rutgers.edu/TechnicalReports.
- [Kim74]J. Kim. State minimization of nondeterministic machines. Technical report, IBM Thomas J. Watson Res. Center, 1974. RC 4896.Google Scholar
- [Mon74]U. Montanari. Networks of constraints: fundamental properties and applications to picture processing. Information Sciences, (7):95–132, 1974.Google Scholar
- [MP95]O. Matz and A. Potthoff. Computing small nondeterministic finite automata. In A. Skou U.H. Engberg, K.G. Larsen, editor, Workshop on Tools and Algorithms for the Construction and Analysis of Systems, pages 74–88. BRICS Notes Series, May 1995.Google Scholar
- [Rev91]Dominique Revuz. Dictionnaires et Lexiques, méthodes et algorithmes. PhD thesis, Université Paris VII, Février 1991.Google Scholar
- [Vem92]N. R. Vempaty. Solving constraint satisfaction problems using finite state automata. In American Association for Artificial Intelligence (AAAI’92), pages 453–458, San Jose, 1992.Google Scholar