On the State Minimization of Nondeterministic Finite Automata

Kameda, Tiko; Weiner, Peter

doi:10.1109/t-c.1970.222994

Cited by 87 publications

(83 citation statements)

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“…A substantial survey by Lombardy and Sakarovitch [12] on the subject of the universal automaton contains its history and a detailed discussion of its properties. We refer the reader to that paper, and mention only that research related to the universal automaton goes back to the 1970's: e.g., in [7] as reported in [1], [8,11].…”

Section: Introductionmentioning

confidence: 99%

Theory of átomata

Brzozowski

Tamm

2014

Theoretical Computer Science

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We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call "átomaton", whose states are the "atoms" of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing theátomaton, and prove that it is isomorphic to the reverse automaton of the minimal deterministic finite automaton (DFA) of the reverse language. We study "atomic" NFAs in which the right language of every state is a union of atoms. We generalize Brzozowski's double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic. We prove that Sengoku's claim that his method always finds a minimal NFA is false.

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Section: Introductionmentioning

confidence: 99%

Theory of átomata

Brzozowski

Tamm

2014

Theoretical Computer Science

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“…) and, therefore, algorithms such as [15][16][17] cannot be used in practice. There are also algorithms which build small NFAs from regular expressions, see [10,6].…”

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Reducing the Size of NFAs by Using Equivalences and Preorders

Ilie

Solis-Oba

Yü

2005

Combinatorial Pattern Matching

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Abstract. The efficiency of regular expression matching algorithms depends very much on the size of the nondeterministic finite automata (NFA) obtained from regular expressions. Reducing the size of these automata by using equivalences has been shown to reduce significantly the search time. We consider the problem of reducing the size of arbitrary NFAs using equivalences and preorders. For equivalences, we give an algorithm to optimally combine equivalent states for reducing the size of the automata. We also show that the problem of optimally using preorders to reduce the size of an automaton is NP-hard.

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“…También, independientemente, aparece implícito en los trabajos de Conway [7] y de Kameda y Weiner [23]. Arnold, Dicky y Nivat en [1] formalizan el concepto y establecen su relevancia en el problema de encontrar autómatas finitos minimales equivalentes a uno dado.…”

Section: Autómata Universalunclassified

“…Kameda y Weiner, en [23], han desarrollado una teoría para abordar el problema de la minimalización. Para cada autómata finito definen una matriz que denominan mapa reducido de estados del autómata, de la que demuestran que es isomorfa a la de cualquier otro autómata finito para el mismo lenguaje, ad-mitiendo tan solo permutaciones de las filas y columnas.…”

Section: Autómatas Finitos Minimalesunclassified

Autómatas finitos: irreducibilidad e Inferencia.

Andrade¹

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On the State Minimization of Nondeterministic Finite Automata

Cited by 87 publications

References 5 publications

Theory of átomata

Theory of átomata

Reducing the Size of NFAs by Using Equivalences and Preorders

Autómatas finitos: irreducibilidad e Inferencia.

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