2018/12/19 by Alexis Linard, Colin de la Higuera, Linard, Alexis +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.FL
paper · pdf · doi:10.48550/arxiv.1812.08269
arxiv created 2018/12/19 · arxiv updated 2018/12/21
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.