The Polynomial Hierarchy - Corelab
The Polynomial Hierarchy - Corelab
The Polynomial Hierarchy - Corelab
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<strong>The</strong> <strong>Polynomial</strong> <strong>Hierarchy</strong><strong>The</strong><strong>Polynomial</strong><strong>Hierarchy</strong>A.AntonopoulosOutlineOptimizationProblemsIntroduction<strong>The</strong> Class DPOracle Classes<strong>The</strong><strong>Polynomial</strong><strong>Hierarchy</strong>DefinitionBasic <strong>The</strong>oremsBPP and PH<strong>Polynomial</strong> <strong>Hierarchy</strong> Definition∆ 0 P = Σ 0 P = Π 0 P = P∆ i+1 P = P Σ i PΣ i+1 P = NP Σ i PΠ i+1 P = coNP Σ i PPH ≡ ⋃ i0Σ i P