A polynomial double reversal minimization algorithm for deterministic finite automata

Parga, Manuel Vázquez de; Garcia, Pedro Castillo; López, Damián

doi:10.1016/j.tcs.2013.03.005

Cited by 12 publications

(8 citation statements)

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“…The second paper, however, shows that it is possible to modify the doublereversal algorithm in such a way that it has polynomial time complexity [14]. The authors present an atomization algorithm, which produces for any NFA N such that N R is a DFA with no unreachable states, an equivalent atomic NFA N A .…”

Section: Extension Of Brzozowski's Theorem On Dfa Minimizationmentioning

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: Extension Of Brzozowski's Theorem On Dfa Minimizationmentioning

confidence: 99%

Theory of átomata

Brzozowski

Tamm

2014

Theoretical Computer Science

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“…Let us now recall a remark in [7]. Note that, if M 1 and M 2 denote unions of atoms, then, trivially, the union of M 1 and M 2 is also a union of atoms, and the following result follows:…”

Section: −1mentioning

confidence: 97%

“…In [6], Brzozowski and Tamm do not propose any algorithm to compute the atomization of an automaton. Recently in [7], we proposed a polynomial-time algorithm that, for any DFA A, outputs an atomic automaton that accepts the reverse language of L(A). This implies that, when the problem is restricted to DFA, it is possible to implement the double-reversal minimization of the input automaton in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

DFA minimization: Double reversal versus split minimization algorithms

Garcia

López

Parga

2015

Theoretical Computer Science

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In this paper, we show the relationship between the two most widely used approaches for the minimization of deterministic finite automata: minimization by split of partitions and minimization by double reversal. Even though the double reversal approach has usually been considered to be unconventional with respect to the more common split approach, we show that any double reversal minimization algorithm can be related to a split minimization algorithm and vice versa.

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“…Essentially, the algorithm computes the automaton D(R(D(R(A)))), where D(A) denotes the determinization of A by the well-known subset construction and R(A) is the reverse automaton of A. Recently, Brzozowski and Tamm proposed a general minimization by double reversal framework [9], thus, the original algorithm by Brzozowski, as well as other recent work [10], became instances within such framework.…”

Section: Introductionmentioning

confidence: 99%

Efficient Deterministic Finite Automata Split-Minimization Derived From Brzozowski's Algorithm

Garcia

López

Parga

2014

Int. J. Found. Comput. Sci.

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Received (Day Month Year) Accepted (Day Month Year) Communicated by (xxxxxxxxxx)Minimization of deterministic finite automata is a classic problem in Computer Science which is still studied nowadays. In this paper, we relate the different split-minimization methods proposed to date, or to be proposed, and the algorithm due to Brzozowski which has been usually set aside in any classification of DF A minimization algorithms. In our work, we first propose a polynomial minimization method derived from a paper by Champarnaud et al. We also show how the consideration of some efficiency improvements on this algorithm lead to obtain an algorithm similar to Hopcroft's classic algorithm. The results obtained lead us to propose a characterization of the set of possible splitters.

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A polynomial double reversal minimization algorithm for deterministic finite automata

Cited by 12 publications

References 2 publications

Theory of átomata

Theory of átomata

DFA minimization: Double reversal versus split minimization algorithms

Efficient Deterministic Finite Automata Split-Minimization Derived From Brzozowski's Algorithm

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