From Glushkov WFAs to \mathbb{K}-Expressions

Caron, Pascal; Flouret, Marianne

doi:10.3233/fi-2011-427

Cited by 9 publications

(2 citation statements)

References 11 publications

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“…As an example, classical regular expressions denote sets of words and regular expressions with multiplicities denote formal series. From a regular expression, solving the membership test (determining whether a word belongs to the denoted language) or the weighting test (determining the weight of a word in the denoted formal series) can be solved, following Kleene theorems [11,17] by computing a finite automaton, such as the position automaton [9,3,5,6].…”

Section: Introductionmentioning

confidence: 99%

Monadic Expressions and their Derivatives [extended version]

Attou¹,

Mignot²,

Miklarz³

et al. 2023

Preprint

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We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear combinations) using the notion of monad. As an example of this generalization advantage, we first introduce a new derivation technique based on the graded module monad and then show an application of this technique to generalize the parsing of expression with capture groups and back references. We also extend operators defining expressions to any n-ary functions over value sets, such as classical operations (like negation or intersection for Boolean weights) or more exotic ones (like algebraic mean for rational weights). Moreover, we present how to compute a (non-necessarily finite) automaton from such an extended expression, using the Colcombet and Petrisan categorical definition of automata. These category theory concepts allow us to perform this construction in a unified way, whatever the underlying monad. Finally, to illustrate our work, we present a Haskell implementation of these notions using advanced techniques of functional programming, and we provide a web interface to manipulate concrete examples.

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Section: Introductionmentioning

confidence: 99%

Monadic Expressions and their Derivatives [extended version]

Attou¹,

Mignot²,

Miklarz³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…As an example, classical regular expressions denote sets of words and regular expressions with multiplicities denote formal series. From a regular expression, solving the membership test (determining whether a word belongs to the denoted language) or the weighting test (determining the weight of a word in the denoted formal series) can be solved, following Kleene theorems [10,17] by computing a finite automaton, such as the position automaton [8,2,4,5].…”

Section: Introductionmentioning

confidence: 99%

Monadic Expressions and their Derivatives

Attou

Mignot

Miklarz

et al. 2022

Electron. Proc. Theor. Comput. Sci.

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We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear combinations) using the notion of monad. As an example of this generalization advantage, we introduce a new derivation technique based on the graded module monad.We also extend operators defining expressions to any n-ary functions over value sets, such as classical operations (like negation or intersection for Boolean weights) or more exotic ones (like algebraic mean for rational weights).Moreover, we present how to compute a (non-necessarily finite) automaton from such an extended expression, using the Colcombet and Petrisan categorical definition of automata. These category theory concepts allow us to perform this construction in a unified way, whatever the underlying monad.Finally, to illustrate our work, we present a Haskell implementation of these notions using advanced techniques of functional programming, and we provide a web interface to manipulate concrete examples.

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In Search of Most Complex Regular Languages

Brzozowski

2012

Implementation and Application of Automata

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Received (Day Month Year) Accepted (Day Month Year) Communicated by (xxxxxxxxxx)Sequences (Ln | n k), called streams, of regular languages Ln are considered, where k is some small positive integer, n is the state complexity of Ln, and the languages in a stream differ only in the parameter n, but otherwise, have the same properties. The following measures of complexity are proposed for any stream: 1) the state complexity n of Ln, that is, the number of left quotients of Ln (used as a reference); 2) the state complexities of the left quotients of Ln; 3) the number of atoms of Ln; 4) the state complexities of the atoms of Ln; 5) the size of the syntactic semigroup of Ln; and the state complexities of the following operations: 6) the reverse of Ln; 7) the star of Ln; 8) union, intersection, difference and symmetric difference of Lm and Ln; and 9) the concatenation of Lm and Ln. A stream that has the highest possible complexity with respect to these measures is then viewed as a most complex stream. The language stream (Un(a, b, c) | n 3) is defined by the deterministic finite automaton with state set {0, 1, . . . , n−1}, initial state 0, set {n−1} of final states, and input alphabet {a, b, c}, where a performs a cyclic permutation of the n states, b transposes states 0 and 1, and c maps state n − 1 to state 0. This stream achieves the highest possible complexities with the exception of boolean operations where m = n. In the latter case, one can use Un(a, b, c) and Un(b, a, c), where the roles of a and b are interchanged in the second language. In this sense, Un(a, b, c) is a universal witness. This witness and its extensions also apply to a large number of combined regular operations.

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From Glushkov WFAs to \mathbb{K}-Expressions

Cited by 9 publications

References 11 publications

Monadic Expressions and their Derivatives [extended version]

Monadic Expressions and their Derivatives [extended version]

Monadic Expressions and their Derivatives

In Search of Most Complex Regular Languages

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