Mind Change Speed-up for Learning Languages from Positive Data

Abstract

Within the frameworks of learning in the limit of indexed classes of recursive languages from positive data and automatic learning in the limit of indexed classes of regular languages (with automatically computable sets of indices), we study the problem of minimizing the maximum number of mind changes F_M(n) by a learner M on all languages with indices not exceeding n. For inductive inference of recursive languages, we establish two conditions under which F_M(n) can be made smaller than any recursive unbounded non-decreasing function. We also establish how F_M(n) is affected if at least one of these two conditions does not hold. In the case of automatic learning, some partial results addressing speeding up the function F_M(n) are obtained.