The Polynomial Hierarchy

The Polynomial Hierarchy (PH) is a layered framework in computational complexity theory that classifies decision problems based on their difficulty and the types of questions needed to solve them. It extends the classes P and NP, introducing levels that involve alternating existential and universal quantifiers over NP problems. Think of it as a hierarchy of increasingly complex problem classes, where each level represents problems that are harder than the previous ones. Understanding the PH helps researchers grasp the deep structure of computational difficulty and the relationships between various complexity classes in theoretical computer science.