In this paper, we tackle the task of graph language learning. We first extend the well-known classes of k-testability and k-testability in the strict sense languages to directed graph languages. Second, we propose a graph automata model for directed acyclic graph languages. This graph automata model is used to propose a grammatical inference algorithm to learn the class of directed acyclic k-testable in the strict sense graph languages. The algorithm runs in polynomial time and identifies this class of languages from positive data.Damián López is partially supported by the Spanish Ministerio de Economía y Competitividad under research project TIN2011-28260-C03-01. Jorge Calera-Rubio and Antonio-Javier Gallego-Sánchez thank the Spanish CICyT for partial support of this work through project TIN2009-14205-C04-01, the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002-506778, and the program CONSOLIDER INGENIO 2010 (CSD2007-00018)
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