Systems that learn: an introduction to learning theory for cognitive and computer scientists
Systems that learn: an introduction to learning theory for cognitive and computer scientists
On the intrinsic complexity of learning
Information and Computation
The intrinsic complexity of language identification
Journal of Computer and System Sciences
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Mitotic Classes in Inductive Inference
SIAM Journal on Computing
Autoreducibility, mitoticity, and immunity
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
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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.