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Using string kernels, languages can be represented as hyperplanes in a high dimensional feature space. We discuss the language-theoretic properties of this formalism with particular reference to the implicit feature maps defined by string kernels, considering the expressive power of the formalism, its closure properties and its relationship to other formalisms. We present a new family of grammatical inference algorithms based on this idea. We demonstrate that some mildly context-sensitivedoi:10.1007/s10994-010-5218-3 fatcat:d6ntfwt4prdofi23n5xplxapyu