Technical Report 08-2 A learning algorithm for multi-dimensional trees, or: Learning beyond context-freeness
نویسنده
چکیده
We generalize a learning algorithm by Drewes and Högberg [1] for regular tree languages based on a learning model proposed by Angluin [2] to recognizable tree languages of arbitrarily many dimensions, so-called multi-dimensional trees. Multi-dimensional trees over multidimensional tree domains have been defined by Rogers [3, 4]. However, since the algorithm by Drewes and Högberg relies on classical finite state automata, these structures have to be represented in another form to make them a suitable input for the algorithm: We give a new representation for multi-dimensional trees which establishes them as a direct generalization of classical trees over a partitioned alphabet, and then show that with this notation Drewes’ and Högberg’s algorithm is able to learn tree languages of arbitrarily many dimensions. Via the correspondence between trees and string languages known as the “yield operation” this is equivalent to the statement that now even some string language classes beyond context-freeness have become learnable with respect to Angluin’s learning model as well.
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