Learning Unions of k-Testable Languages

Alexis Linard; Colin de la Higuera; Frits Vaandrager

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arXiv · 1812.08269

Learning Unions of k-Testable Languages

Alexis Linard·Colin de la Higuera·Frits Vaandrager

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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 Σ, and the lattice of k-TSS languages over Σ. 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.

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Alexis Linard, Colin de la Higuera, Frits Vaandrager. 2018-12-19. Learning Unions of k-Testable Languages. https://arxiv.org/abs/1812.08269

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