Simplifying Regular Expressions

Gruber, Hermann; Gulan, Stefan

doi:10.1007/978-3-642-13089-2_24

Cited by 10 publications

(9 citation statements)

References 14 publications

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“…We consider the grammar for regular expressions proposed by Gruber and Gulan in Refs. [12,13], which has the major advantage of avoiding many redundant expressions built with the symbols ε and ∅. Given an alphabet Σ = {σ 1 , .…”

Section: Regular Expressions and Nfasmentioning

confidence: 99%

“…An improved version of this construction was redefined by Ilie and Yu, and called the ε-follow automaton. Gulan, Fernau and Gruber [12][13][14] studied the optimal (worst-case) size for all known constructions from regular expressions to ε-NFAs. It turns out that the optimal construction corresponds to the conversion of a regular expression in strong star normal form into an ε-follow automaton.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On Average Behaviour of Regular Expressions in Strong Star Normal Form

Broda

Machiavelo

Moreira

et al. 2019

Int. J. Found. Comput. Sci.

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For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to get the required information for the asymptotic estimates with an indirect use of the existence of Puiseux expansions at singularities. We study, asymptotically and on average, the alphabetic size, the size of the [Formula: see text]-follow automaton and of the position automaton, as well as the ratio and the size of these expressions to standard regular expressions.

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Section: Regular Expressions and Nfasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Average Behaviour of Regular Expressions in Strong Star Normal Form

Broda

Machiavelo

Moreira

et al. 2019

Int. J. Found. Comput. Sci.

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show abstract

“…The alphabetic width awidth is the total number of alphabetic symbols from Σ (counted with multiplicity) [27,83]. Relations between these measures have been studied, e.g., in [27,28,42,66]. Theorem 2 Let L ⊆ Σ * be a regular language.…”

Section: Measures On Finite Automata and Regular Expressionsmentioning

confidence: 99%

“…-operator and instead forbid the use of / 0 and ε inside non-atomic expressions. This is sometimes more convenient, since one avoids unnecessary redundancy already at the syntactic level [42]. width n. In r we attach subscripts to each letter referring to its position (counted from left to right) in r. This yields a marked expression r with distinct input symbols over an alphabet Σ that contains all letters that occur in r. To simplify our presentation we assume that the same notation is used for unmarking, i.e., r = r. Then in order to describe the position automaton we need to define the following sets of positions on the marked expression.…”

Section: From Regular Expressions To Finite Automatamentioning

confidence: 99%

From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

Gruber

Holzer²

2014

Electron. Proc. Theor. Comput. Sci.

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The equivalence of finite automata and regular expressions dates back to the seminal paper of Kleene on events in nerve nets and finite automata from 1956. In the present paper we tour a fragment of the literature and summarize results on upper and lower bounds on the conversion of finite automata to regular expressions and vice versa. We also briefly recall the known bounds for the removal of spontaneous transitions (ε-transitions) on non-ε-free nondeterministic devices. Moreover, we report on recent results on the average case descriptional complexity bounds for the conversion of regular expressions to finite automata and brand new developments on the state elimination algorithm that converts finite automata to regular expressions.

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“…An improved version of this construction was redefined by Ilie and Yu, and called the ε-follow automaton. Gulan, Fernau and Gruber [12,10,11] studied the optimal (worst-case) size for all known constructions from regular expressions to ε-NFAs. It turns out that the optimal construction corresponds to the conversion of a regular expression in strong star normal form into an ε-follow automaton.…”

Section: Introductionmentioning

confidence: 99%

On the Average Complexity of Strong Star Normal Form

Broda

Machiavelo

Moreira

et al. 2017

Descriptional Complexity of Formal Systems

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For regular expressions in (strong) star normal form a large set of efficient algorithms is known, from conversions into finite automata to characterisations of unambiguity. In this paper we study the average complexity of this class of expressions using analytic combinatorics. As it is not always feasible to obtain explicit expressions for the generating functions involved, here we show how to get the required information for the asymptotic estimates with an indirect use of the existence of Puiseux expansions at singularities. We study, asymptotically and on average, the alphabetic size, the size of the ε-follow automaton and the ratio of these expressions to standard regular expressions.

show abstract

Simplifying Regular Expressions

Cited by 10 publications

References 14 publications

On Average Behaviour of Regular Expressions in Strong Star Normal Form

On Average Behaviour of Regular Expressions in Strong Star Normal Form

From Finite Automata to Regular Expressions and Back—A Summary on Descriptional Complexity

On the Average Complexity of Strong Star Normal Form

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