5.4.3 Vacillatory Learning
Definition
5.11
Vacillatory Learning (\(\mathrm{Vex}\))
A learner vacillatorily identifies \(L\) if it eventually oscillates among finitely many indices \(e_1, \ldots , e_k\), all satisfying \(W_{e_i} = L\). The learner never settles on a single index, but all its eventual outputs are extensionally correct and drawn from a finite set.
Vacillatory learning sits between \(\mathbf{Ex}\) (which requires convergence to a single index) and \(\mathbf{BC}\) (which allows infinitely many correct indices). It is strictly more powerful than \(\mathbf{Ex}\) and strictly less powerful than \(\mathbf{BC}\).