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Improved Grammar-Based Compressed Indexes

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Francisco Claude, Gonzalo Navarro

Data Structures and Algorithms · Submitted 20 Oct 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar.

how it is stated · asserted 1.00 read the record →

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arXiv ID1110.4493 (version 1)
Pith IDIVOWOYBZ, Pith's permanent record of this paper and its review
CitationFrancisco Claude, Gonzalo Navarro. "Improved Grammar-Based Compressed Indexes." arXiv:1110.4493 (2011). https://pith.science/paper/IVOWOYBZ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,951 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of $T$ takes $N\lg n$ bits of space. Our representation requires $2N\lg n + N\lg u + \epsilon\, n\lg n + o(N\lg n)$ bits of space, for any $0<\epsilon \le 1$. It can find the positions of the $occ$ occurrences of a pattern of length $m$ in $T$ in $O((m^2/\epsilon)\lg (\frac{\lg u}{\lg n}) +occ\lg n)$ time, and extract any substring of length $\ell$ of $T$ in time $O(\ell+h\lg(N/h))$, where $h$ is the height of the grammar tree.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. contribution 1.00 0.95 0.83 asserted 1.00
s1 Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of $T$ takes $N\lg n$ bits of space. background 1.00 0.14 0.04 asserted 1.00
s2 Our representation requires $2N\lg n + N\lg u + \epsilon\, n\lg n + o(N\lg n)$ bits of space, for any $0<\epsilon \le 1$. result 0.73 0.93 0.11 asserted 1.00
s3 It can find the positions of the $occ$ occurrences of a pattern of length $m$ in $T$ in $O((m^2/\epsilon)\lg (\frac{\lg u}{\lg n}) +occ\lg n)$ time, and extract any substring of length $\ell$ of $T$ in time $O(\ell+h\lg(N/h))$, where $h$ is the height of the grammar tree. result 0.69 0.93 0.26 asserted 0.92

What kind of paper the classifier reports this is: method or tool 0.97 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured as the sum of the lengths of the right hands of the rules), a basic grammar-based representation of $T$ takes $N\lg n$ bits of space. Our representation requires $2N\lg n + N\lg u + \epsilon\, n\lg n + o(N\lg n)$ bits of space, for any $0<\epsilon \le 1$. It can find the positions of the $occ$ occurrences of a pattern of length $m$ in $T$ in $O((m^2/\epsilon)\lg (\frac{\lg u}{\lg n}) +occ\lg n)$ time, and extract any substring of length $\ell$ of $T$ in time $O(\ell+h\lg(N/h))$, where $h$ is the height of the grammar tree.

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