The Inference of Tree Languages from Finite Samples: An Algebraic Approach

Abstract The theory presented in this paper is intended as a mathematical basis for the understanding of methods of inferring tree languages from finite samples. Many such methods given in the literature involve, at least implicitly, the construction of some kind of a nondeterministic quotient recognizer. We define and study in a general form such quotients of algebras and tree recognizers. Some abstract families of inference algorithms are considered, and methods presented in the literature are discussed in relation to these. Since strings may be regarded as unary trees, the results of the paper apply also to string languages.

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