Learning Disjunctions of Predicates

TL;DR

This paper introduces an efficient algorithm for learning disjunctions of boolean functions from membership queries, with applications in program synthesis, especially when requirements are learned interactively from users.

Contribution

The paper presents a new algorithm for learning disjunctions of boolean functions with near-optimal query complexity, applicable to specific function classes like halfspaces and inequalities.

Findings

Algorithm asks at most |F| * OPT(F_∨) membership queries.

Runs in polynomial time for certain function classes.

Enables practical program synthesis by reducing user queries.

Abstract

Let $F$ be a set of boolean functions. We present an algorithm for learning $F_\vee := \{\vee_{f\in S} f \mid S \subseteq F\}$ from membership queries. Our algorithm asks at most $|F| \cdot OPT(F_\vee)$ membership queries where $OPT(F_\vee)$ is the minimum worst case number of membership queries for learning $F_\vee$. When $F$ is a set of halfspaces over a constant dimension space or a set of variable inequalities, our algorithm runs in polynomial time. The problem we address has practical importance in the field of program synthesis, where the goal is to synthesize a program that meets some requirements. Program synthesis has become popular especially in settings aiming to help end users. In such settings, the requirements are not provided upfront and the synthesizer can only learn them by posing membership queries to the end user. Our work enables such synthesizers to learn the exact requirements while bounding the number of membership queries.