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 ω ω and \(\omega^{\omega^{\omega}}\). 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 ω ω. 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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de Brecht, M., Yamamoto, A. (2006). Mind Change Complexity of Inferring Unbounded Unions of Pattern Languages from Positive Data. In: Balcázar, J.L., Long, P.M., Stephan, F. (eds) Algorithmic Learning Theory. ALT 2006. Lecture Notes in Computer Science(), vol 4264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11894841_13
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DOI: https://doi.org/10.1007/11894841_13
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