Non-learnable classes of Boolean formulae that are closer under variable permutation

The authors first present a class of expansions in a series of Bernoulli polyomials and then show how this general result can be applied to yield various (known or new) polynomial expansions. The corresponding expansion problem involving the Euler ...

We study which classes of recursive functions satisfy that their union with any other explanatorily learnable class of recursive functions is again explanatorily learnable. We provide sufficient criteria for classes of recursive functions to satisfy ...

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In ...