Recall that the Polynomial Hierarchy (PH) is a hierarchy of complexity classes that generalize the classes P, NP, and co-NP. It is defined using oracle machines and alternations of quantifiers.

The k-th level of the PH, denoted Σₖᵖ, consists of problems solvable by a polynomial-time Turing machine with k alternations of existential and universal quantifiers, starting with existential. The classes Πₖᵖ and Δₖᵖ are defined similarly with alternating quantifiers starting with universal and polynomial-time bounds, respectively.

To relate PH to P/NP, observe that Σ₁ᵖ = NP and Π₁ᵖ = co-NP. The entire PH collapses to a finite level (e.g., PH = Σ₂ᵖ) if and only if P = NP. Investigate how oracle access and quantifier alternations influence this relationship.