Mind Change Complexity of Inferring Unbounded Unions of Pattern Languages from Positive Data

Authors: Matthew de Brecht and Akihiro Yamamoto

Source: Algorithmic Learning Theory, 17th International Conference, ALT 2006, Barcelona, October 2006, Proceedings, (José L. Balcázar, Phil Long and Frank Stephan, Eds.), Lecture Notes in Artificial Intelligence 4264, pp. 124 - 138, Springer 2006.

Abstract. This paper gives a proof that the class of unbounded unions of languages of regular patterns with constant segment length bound is inferable from positive data with mind change bound between ωω and ωωω. We give a very tight bound on the mind change complexity based on the length of the constant segments and the size of the alphabet of the pattern languages. This is, to the authors' knowledge, the first time a natural class of languages has been shown to be inferable with mind change complexity above ωω. The proof uses the notion of closure operators on a class of languages, and also uses the order type of well-partial-orderings to obtain a mind change bound. The inference algorithm presented can be easily applied to a wide range of classes of languages. Finally, we show an interesting connection between proof theory and mind change complexity.

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