Glushkov Construction For Series: The Non Commutative Case

Caron, Pascal; Flouret, Marianne

doi:10.1080/0020716021000038992

Cited by 13 publications

(7 citation statements)

References 13 publications

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“…An algorithm given by Glushkov [8] for computing an automaton with n + 1 states from a regular expression of litteral length n has been extended to semirings K by the authors [4]. Informally, the principle is to associate exactly one state in the computed automaton to each occurrence of letters in the expression.…”

Section: Extended Glushkov Constructionmentioning

confidence: 99%

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Algorithms for Glushkov K-graphs

Caron,

Flouret

2009

Preprint

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The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expression-to-automaton algorithmic short cut [8]. The Glushkov graphs have been characterized [5] in terms of simple graph theoretical properties and certain reduction rules. We show how to carry, under certain restrictions, this characterization over to the weighted Glushkov graphs. With the weights in a semiring K, they are defined as the transition Glushkov K-graphs of the Weighted Finite Automata (WFA) obtained by the generalized Glushkov construction [4] from the K-expressions. It works provided that the semiring K is factorial and the K-expressions are in the so called star normal form (SNF) of Brüggeman-Klein [2]. The restriction to the factorial semiring ensures to obtain algorithms. The restriction to the SNF would not be necessary if every K-expressions were equivalent to some with the same litteral length, as it is the case for the boolean semiring B but remains an open question for a general K.

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Section: Extended Glushkov Constructionmentioning

confidence: 99%

“…Many research works have focused on producing a small WFA. For example, Caron and Flouret have extended the Glushkov construction to WFAs [4]. Champarnaud et al have designed a quadratic algorithm [?]…”

Section: Introductionmentioning

confidence: 99%

Algorithms for Glushkov K-graphs

Caron,

Flouret

2009

Preprint

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“…As we recall in Section 3 below the position automaton may be inductively defined by means of operations on automata of a certain kind that we call standard automata. The definition and computation of the position automaton readily generalises to weighted expressions [5] and, even more easily as there is nothing to change, to expressions over non free monoids.…”

Section: Introductionmentioning

confidence: 99%

Derived Terms Without Derivation a Shifted Perspective on the Derived-Term Automaton

Lombardy¹,

Sakarovitch²

2021

JCC

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“…For the conversion of weighted regular expressions into weighted automata there are principally three algorithms. The first one is due to Caron and Flouret [4]. Their algorithm works recursively on a subset of weighted regular expressions and produces the position automaton.…”

Section: Introductionmentioning

confidence: 99%

Efficient weighted expressions conversion

Ouardi

Ziadi

2007

RAIRO-Theor. Inf. Appl.

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J. Hromkovic et al. have given an elegant method to convert a regular expression of size n into an ε-free nondeterministic finite automaton having O(n) states and O(n log 2 (n)) transitions. This method has been implemented efficiently in O(n log 2 (n)) time by C. Hagenah and A. Muscholl. In this paper we extend this method to weighted regular expressions and we show that it can be achieved in O(n log 2 (n)) time.

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Glushkov Construction For Series: The Non Commutative Case

Cited by 13 publications

References 13 publications

Algorithms for Glushkov K-graphs

Algorithms for Glushkov K-graphs

Derived Terms Without Derivation a Shifted Perspective on the Derived-Term Automaton

Efficient weighted expressions conversion

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