eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-29
10:1
10:21
10.4230/LIPIcs.CONCUR.2024.10
article
Passive Learning of Regular Data Languages in Polynomial Time and Data
Balachander, Mrudula
1
https://orcid.org/0000-0001-8688-3550
Filiot, Emmanuel
1
https://orcid.org/0000-0002-2520-5630
Gentilini, Raffaella
2
https://orcid.org/0000-0002-4400-3137
Université libre de Bruxelles, Belgium
Universitá degli Studi di Perugia, Italy
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol311-concur2024/LIPIcs.CONCUR.2024.10/LIPIcs.CONCUR.2024.10.pdf
Register automata
passive learning
automata over infinite alphabets