New Learning and Testing Problems for Read-Once Functions

TL;DR

This paper explores new learning and testing problems for read-once functions, identifying the boundary between polynomial and exponential complexities for various query types.

Contribution

It introduces novel problems and analyzes their complexity, establishing clear boundaries between feasible and infeasible cases for read-once function learning and testing.

Findings

Identified polynomial-exponential complexity boundaries

Analyzed classical and new query-based learning problems

Provided complexity classifications for read-once functions

Abstract

In the paper, we consider several types of queries for classical and new problems of learning and testing read-once functions. In several cases, the border between polynomial and exponential complexities is obtained.