## Journal of Symbolic Logic

### Anomalous Vacillatory Learning

Achilles A. Beros

#### 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$^*_2 \setminus \mbox{TxtFext}^*_*$.

#### Article information

Source
J. Symbolic Logic Volume 78, Issue 4 (2013), 1183-1188.

Dates
First available in Project Euclid: 5 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1388954000

Digital Object Identifier
doi:10.2178/jsl.7804090

Mathematical Reviews number (MathSciNet)
MR3156518

Zentralblatt MATH identifier
1290.68061

#### Citation

Beros, Achilles A. Anomalous Vacillatory Learning. J. Symbolic Logic 78 (2013), no. 4, 1183--1188. doi:10.2178/jsl.7804090. https://projecteuclid.org/euclid.jsl/1388954000