## Learning unions of $$k$$-testable languages.(English)Zbl 1425.68150

Martín-Vide, Carlos (ed.) et al., Language and automata theory and applications. 13th international conference, LATA 2019, St. Petersburg, Russia, March 26–29, 2019, Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11417, 328-339 (2019).
Summary: A classical problem in grammatical inference is to identify a language from a set of examples. In this paper, we address the problem of identifying a union of languages from examples that belong to several different unknown languages. Indeed, decomposing a language into smaller pieces that are easier to represent should make learning easier than aiming for a too generalized language. In particular, we consider $$k$$-testable languages in the strict sense $$(k$$-TSS). These are defined by a set of allowed prefixes, infixes (sub-strings) and suffixes that words in the language may contain. We establish a Galois connection between the lattice of all languages over alphabet $$\varSigma$$, and the lattice of $$k$$-TSS languages over $$\varSigma$$. We also define a simple metric on $$k$$-TSS languages. The Galois connection and the metric allow us to derive an efficient algorithm to learn the union of $$k$$-TSS languages. We evaluate our algorithm on an industrial dataset and thus demonstrate the relevance of our approach.
For the entire collection see [Zbl 1423.68031].

### MSC:

 68Q32 Computational learning theory 06A15 Galois correspondences, closure operators (in relation to ordered sets) 68Q45 Formal languages and automata
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