Anomalous Vacillatory Learning

Abstract

In 1986, Osherson, Stob and Weinstein asked whether two variants of anomalous vacillatory learning, TxtFex$^*_*$ and TxtFext$^*_*$, could be distinguished [3]. In both, a machine is permitted to vacillate between a finite number of hypotheses and to make a finite number of errors. TxtFext$^*_*$-learning requires that hypotheses output infinitely often must describe the same finite variant of the correct set, while TxtFex$^*_*$-learning permits the learner to vacillate between finitely many different finite variants of the correct set. In this paper we show that TxtFex$^*_*$ $\neq$ TxtFext$^*_*$, thereby answering the question posed by Osherson, et al. We prove this in a strong way by exhibiting a family in TxtFex$^*_2 \setminus \mbox{TxtFext}^*_*$.