Context-Free Grammars with Lookahead

Miyazaki, Takuro; Minamide, Yasuhiko

doi:10.1007/978-3-030-68195-1_16

Cited by 2 publications

(6 citation statements)

References 18 publications

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“…We review CFGLAs and their original semantics [16]. In addition, we show the relationship between CFGLA and CFGRC, which is not discussed in the previous paper [16].…”

Section: Context-free Grammars With Lookaheadmentioning

confidence: 97%

“…The language L(G 3 ) is {a k n | n ≥ 0}. The language class of CFGLA is closed under union, intersection, complement, marked concatenation, and marked Kleene star [16]. That is, for two languages of CFGLA L, L ′ ⊆ Σ * and a letter # Σ,…”

Section: Context-free Grammars With Lookaheadmentioning

confidence: 99%

“…Semantically, PEG is characterized by the derivation. For CFGLA, the derivation (e, x) ⇒ O that is an extension of the PEG's derivation is defined by the following, where e is an expression, x is an input string, and O is a set of the remaining input string [16].…”

Section: Context-free Grammars With Lookaheadmentioning

confidence: 99%

“…For example, this can be used to check whether a given string contains uppercase and lowercase letters and digits. Lookahead is used in the traditional theory of parsing and other areas of formal language theory [6], [9], [16], [22], [23].…”

Section: Introductionmentioning

confidence: 99%

“…Context-free grammars with lookahead (CFGLAs) [16] are minamide@is.titech.ac.jp context-free grammars (CFGs) with positive and negative lookahead. As we describe in detail later, CFGLA can be regarded as a system of equations, and its semantics is given by the limit of iterations from the empty set.…”

Section: Introductionmentioning

confidence: 99%

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Derivatives of Context-free Grammars with Lookahead

Miyazaki

Minamide

2023

Journal of Information Processing

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Context-free grammars with lookahead (CFGLAs) are context-free grammars with positive and negative lookahead. In this paper, we develop a recognition algorithm for CFGLA by combining derivatives of context-free grammars and derivatives of regular expressions with lookahead. The original semantics of CFGLA has some problems, and the recognition algorithm does not run in polynomial time. We introduce better semantics with the least fixed point of pairs of lower and upper bounds. Under the new semantics, the recognition algorithm runs in O(n 3 |G|) time and O(n 2 |G|) space for an input string of the length n and a given CFGLA G.

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“…We review CFGLAs and their original semantics [16]. In addition, we show the relationship between CFGLA and CFGRC, which is not discussed in the previous paper [16].…”

Section: Context-free Grammars With Lookaheadmentioning

confidence: 97%

Section: Context-free Grammars With Lookaheadmentioning

confidence: 99%

Section: Context-free Grammars With Lookaheadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Derivatives of Context-free Grammars with Lookahead

Miyazaki

Minamide

2023

Journal of Information Processing

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Efficient Matching of Regular Expressions with Lookaround Assertions

Mamouras,

Chattopadhyay

2024

Proc. ACM Program. Lang.

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Regular expressions have been extended with lookaround assertions, which are subdivided into lookahead and lookbehind assertions. These constructs are used to refine when a match for a pattern occurs in the input text based on the surrounding context. Current implementation techniques for lookaround involve backtracking search, which can give rise to running time that is super-linear in the length of input text. In this paper, we first consider a formal mathematical semantics for lookaround, which complements the commonly used operational understanding of lookaround in terms of a backtracking implementation. Our formal semantics allows us to establish several equational properties for simplifying lookaround assertions. Additionally, we propose a new algorithm for matching regular expressions with lookaround that has time complexity O ( m · n ), where m is the size of the regular expression and n is the length of the input text. The algorithm works by evaluating lookaround assertions in a bottom-up manner. Our algorithm makes use of a new notion of nondeterministic finite automata (NFAs), which we call oracle-NFAs. These automata are augmented with epsilon-transitions that are guarded by oracle queries that provide the truth values of lookaround assertions at every position in the text. We provide an implementation of our algorithm that incorporates three performance optimizations for reducing the work performed and memory used. We present an experimental comparison against PCRE and Java’s regex library, which are state-of-the-art regex engines that support lookaround assertions. Our experimental results show that, in contrast to PCRE and Java, our implementation does not suffer from super-linear running time and is several times faster.

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Context-Free Grammars with Lookahead

Cited by 2 publications

References 18 publications

Derivatives of Context-free Grammars with Lookahead

Derivatives of Context-free Grammars with Lookahead

Efficient Matching of Regular Expressions with Lookaround Assertions

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