Learning Disjunctions of Predicates
This work addresses a practical problem in program synthesis, enabling synthesizers to learn exact requirements from end users with bounded query complexity, though it is incremental as it builds on existing query learning frameworks.
The paper tackles the problem of learning disjunctions of boolean functions from membership queries, presenting an algorithm that asks at most |F| * OPT(F_∨) queries, where OPT(F_∨) is the minimum worst-case number, and runs in polynomial time for specific sets like halfspaces in constant dimensions or variable inequalities.
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.