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We propose 10 diﬀerent open problems in the ﬁeld of grammatical inference. In all cases, problems are theoretically oriented but correspond to practical questions. They cover the areas of polynomial learning models, learning from ordered alphabets, learning deterministic Pomdps, learning negotiation processes, learning from context-free background knowledge. 1 Introduction Results in grammatical inference can usually be of use in several diﬀerent domains. For instance progress in learning stochastic ﬁnite state machines and grammars has occurred because of eﬀorts for computational biology [1,2], or speech recognition , or even document representation .