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The Trichotomy of Regular Property Testing

Authors Gabriel Bathie , Nathanaël Fijalkow , Corto Mascle

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ACM Subject Classification
  • Theory of computation → Regular languages
Keywords
  • property testing
  • regular languages

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Abstract

Property testing is concerned with the design of algorithms making a sublinear number of queries to distinguish whether the input satisfies a given property or is far from having this property. A seminal paper of Alon, Krivelevich, Newman, and Szegedy in 2001 introduced property testing of formal languages: the goal is to determine whether an input word belongs to a given language, or is far from any word in that language. They constructed the first property testing algorithm for the class of all regular languages. This opened a line of work with improved complexity results and applications to streaming algorithms. In this work, we show a trichotomy result: the class of regular languages can be divided into three classes, each associated with an optimal query complexity. Our analysis yields effective characterizations for all three classes using so-called minimal blocking sequences, reasoning directly and combinatorially on automata.

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Gabriel Bathie, Nathanaël Fijalkow, and Corto Mascle. The Trichotomy of Regular Property Testing. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 141:1-141:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.141

Author Details

Gabriel Bathie
  • LaBRI, Université de Bordeaux, France
  • DIENS, Paris, France
Nathanaël Fijalkow
  • LaBRI, CNRS, Université de Bordeaux, France
Corto Mascle
  • LaBRI, Université de Bordeaux, France
  • MPI-SWS, Kaiserslautern, Germany

Funding

  • Bathie, Gabriel: Partially funded by the grant ANR-20-CE48-0001 from the French National Research Agency.

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