Abstract
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.
This research is supported by the Dutch Technology Foundation (STW) under the Robust CPS program (project 12693).
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Notes
- 1.
For missing proofs, see http://arxiv.org/abs/1812.08269.
- 2.
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Linard, A., de la Higuera, C., Vaandrager, F. (2019). Learning Unions of k-Testable Languages. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_24
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