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Dynamic Direct Access of MSO Query Evaluation over Strings

Authors Pierre Bourhis , Florent Capelli , Stefan Mengel , Cristian Riveros

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Author Details

Pierre Bourhis
  • Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
Florent Capelli
  • Univ. Artois, CNRS, UMR 8188, Centre de Recherche en Informatique de Lens (CRIL), F-62300 Lens, France
Stefan Mengel
  • Univ. Artois, CNRS, UMR 8188, Centre de Recherche en Informatique de Lens (CRIL), F-62300 Lens, France
Cristian Riveros
  • Pontificia Universidad Católica de Chile, Santiago, Chile
  • Millennium Institute for Foundational Research on Data, Santiago, Chile

Funding

This work was partially funded by ANR projects CQFD 18-CE23-0003, EQUUS ANR-19-CE48-0019 and KCODA ANR-20-CE48-0004, by ANID - Millennium Science Initiative Program - Code ICN17_002, by ANID Fondecyt Regular project 1230935, and by the Alexander von Humboldt Foundation.

Acknowledgements

This work benefited from https://www.dagstuhl.de/seminars/seminar-calendar/seminar-details/24032, Representation, Provenance, and Explanations in Database Theory and Logic.

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Pierre Bourhis, Florent Capelli, Stefan Mengel, and Cristian Riveros. Dynamic Direct Access of MSO Query Evaluation over Strings. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICDT.2025.26

Abstract

We study the problem of evaluating a Monadic Second Order (MSO) query over strings under updates in the setting of direct access. We present an algorithm that, given an MSO query with first-order free variables represented by an unambiguous variable-set automaton 𝒜 with state set Q and variables X and a string s, computes a data structure in time 𝒪(|Q|^ω⋅ |X|² ⋅ |s|) and, then, given an index i retrieves, using the data structure, the i-th output of the evaluation of 𝒜 over s in time 𝒪(|Q|^ω ⋅ |X|³ ⋅ log(|s|)²) where ω is the exponent for matrix multiplication. Ours is the first efficient direct access algorithm for MSO query evaluation over strings; such algorithms so far had only been studied for first-order queries and conjunctive queries over relational data.
Our algorithm gives the answers in lexicographic order where, in contrast to the setting of conjunctive queries, the order between variables can be freely chosen by the user without degrading the runtime. Moreover, our data structure can be updated efficiently after changes to the input string, allowing more powerful updates than in the enumeration literature, e.g. efficient deletion of substrings, concatenation and splitting of strings, and cut-and-paste operations. Our approach combines a matrix representation of MSO queries and a novel data structure for dynamic word problems over semi-groups which yields an overall algorithm that is elegant and easy to formulate.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database theory
Keywords
  • Query evaluation
  • direct access
  • MSO queries

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