Abstract
A class \(\mathcal{L}\) is called mitotic if it admits a splitting \(\mathcal{L}_0,\mathcal{L}_1\) such that \(\mathcal{L},\mathcal{L}_0,\mathcal{L}_1\) are all equivalent with respect to a certain reducibility. Such a splitting might be called a symmetric splitting. In this paper we investigate the possibility of constructing a class which has a splitting and where any splitting of the class is a symmetric splitting. We call such a class a symmetric class. In particular we construct an incomplete symmetric BC-learnable class with respect to strong reducibility. We also introduce the notion of very strong reducibility and construct a complete symmetric BC-learnable class with respect to very strong reducibility. However, for EX-learnability, it is shown that there does not exist a symmetric class with respect to any weak, strong or very strong reducibility.
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Li, H., Stephan, F. (2010). Splitting of Learnable Classes. In: Sempere, J.M., García, P. (eds) Grammatical Inference: Theoretical Results and Applications. ICGI 2010. Lecture Notes in Computer Science(), vol 6339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15488-1_10
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DOI: https://doi.org/10.1007/978-3-642-15488-1_10
Publisher Name: Springer, Berlin, Heidelberg
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