Splitting of Learnable Classes
نویسندگان
چکیده
A class L is called mitotic if it admits a splitting L0,L1 such that L,L0,L1 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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