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Passive Learning of Regular Data Languages in Polynomial Time and Data

Authors Mrudula Balachander , Emmanuel Filiot , Raffaella Gentilini

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Author Details

Mrudula Balachander
  • Université libre de Bruxelles, Belgium
Emmanuel Filiot
  • Université libre de Bruxelles, Belgium
Raffaella Gentilini
  • Universitá degli Studi di Perugia, Italy

Funding

  • Balachander, Mrudula: PhD funded by F.R.S.-FNRS.
  • Filiot, Emmanuel: Senior research associate of the F.R.S.-FNRS. His contribution to this work was partly funded by the FNRS MIS project F451019F and the FNRS PDR project T.0117.24.

Acknowledgements

We thank Marie Tcheng for spotting some issue in the characterization of completability in a preliminary version of this paper.

Cite AsGet BibTex

Mrudula Balachander, Emmanuel Filiot, and Raffaella Gentilini. Passive Learning of Regular Data Languages in Polynomial Time and Data. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CONCUR.2024.10

Abstract

A regular data language is a language over an infinite alphabet recognized by a deterministic register automaton (DRA), as defined by Benedikt, Ley and Puppis. The later model, which is expressively equivalent to the deterministic finite-memory automata introduced earlier by Francez and Kaminsky, enjoys unique minimal automata (up to isomorphism), based on a Myhill-Nerode theorem. In this paper, we introduce a polynomial time passive learning algorithm for regular data languages from positive and negative samples. Following Gold’s model for learning languages, we prove that our algorithm can identify in the limit any regular data language L, i.e. it returns a minimal DRA recognizing L if a characteristic sample set for L is provided as input. We prove that there exist characteristic sample sets of polynomial size with respect to the size of the minimal DRA recognizing L. To the best of our knowledge, it is the first passive learning algorithm for data languages, and the first learning algorithm which is fully polynomial, both with respect to time complexity and size of the characteristic sample set.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Automata over infinite objects
Keywords
  • Register automata
  • passive learning
  • automata over infinite alphabets

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