Theoretical study and implementation of the canonical automaton

• Autorzy: Champarnaud J-M. , Coulon F.
• Języki publikacji: EN

Abstrakty

EN

We can represent the canonical automaton of a language as the smallest automaton which contains any other automaton recognizing this language, providing equivalent states are merged. Indeed, the canonical automaton appears to be a good representative element in the equivalence class of non-deterministic automata recognizing a given language. Our aim is to provide a detailed description of the canonical automaton based on the notions of syntactical rectangle and characteristic event. In our approach, a state of the canonical automaton of a language L is associated with a rectangle (L,R) Í S*×S*, which is maximal w.r.t. the property L.R Í L. We explicit the link with other characterizations, like considering a state as a residual intersection which was given by Arnold et al., and the fundamental automaton defined by Matz and Potthoff. In particular, we pretend that the construction of the canonical automaton has the same time complexity as the construction of the fundamental automaton. Our last section briefly discusses the problem of searching minimal NFAs using the canonical automaton.

Słowa kluczowe

EN

canonical / fundamental automaton; Nondeterministic Finite Automata (NFA); NFA minimization; grid cover; characteristic event

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2003
• Tom: Vol. 55, nr 1
• Strony: 23--38
• Opis fizyczny: bibliogr. 10 poz.

Twórcy

autor

Champarnaud J-M.

autor

Coulon F.

• Université de Rouen, LIFAR, 76821 Mont-Saint-Aignan Cedex France,,

Bibliografia

• [1] Amilhastre, J.: Repr´esentation par automate d’ensemble de solutions de probl`emes de satisfaction de contraintes, Ph.D. Thesis, Universit´e Montpellier II, 1999.
• [2] Arnold, A., Dicky, A., Nivat, M.: A note about minimal non-deterministic automata, Bulletin of the EATCS, number 47, June 1992, 166–169.
• [3] Brzozowski, J. A.: Canonical Regular Expressions and Minimal State Graphs for Definite Events, Mathematical Theory of Automata, MRI Symposia Series, 12, 1962, 529–561.
• [4] Calude, C. S., Calude, E., Khoussainov, B.: Finite nondeterministic automata: Simulation and minimality, Theoretical Computer Science, 242(1–2), 2000, 219–235.
• [5] Carrez, C.: On The Minimalization of Non-Deterministic Automaton, Technical report, Laboratoire de Calcul de la Facult´e des Sciences de l’Universit´e de Lille, 1970.
• [6] Courcelle, B., Niwinski, D., Podelski, A.: A Geometrical View of the Determinization and Minimization of Finite-State Automata, Mathematical Systems Theory 24, 1991.
• [7] Kameda, T., Weiner, P.: On the State Minimization of Nondeterministic Finite Automata, IEEE Trans. Comp., C(19), 1970, 617–627.
• [8] Kleene, S. C.: Representation of events in nerve nets and finite automata, Automata Studies, 1996, 2–42.
• [9] Matz, O., Potthoff, A.: Computing Small Nondeterministic Finite Automata, Tools and Algorithms for the Construction and Analysis of Systems – TACAS 95, volume NS-95-2, 1995, 74–88.
• [10] Yu, S.: Regular Languages, Handbook of Formal Languages, Volume I, Word, Language, Grammar (G. Rozenberg, A. Salomaa, Eds.), Springer, Berlin, 1997.