From Exact Learning to Computing Boolean Functions and Back Again

TL;DR

This paper explores the relationship between complexity measures in Boolean function evaluation and exact learning, aiming to establish bounds and connections between these two areas.

Contribution

It introduces a framework to relate complexity measures of Boolean functions with learning dimensions, bridging the gap between evaluation and learning tasks.

Findings

Established bounds linking decision tree and teaching dimensions

Identified conditions where complexity measures coincide

Provided insights into the complexity of testing versus learning Boolean functions

Abstract

The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension, extended teaching dimension). The high level motivation is to discover non-trivial relations between exact learning of an unknown concept and testing whether an unknown concept is part of a concept class or not. Concretely, the goal is to provide lower and upper bounds of complexity measures for one problem type in terms of the other.