The Polynomial Hierarchy - Corelab

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NP[log n]The Class PThePolynomialHierarchyA.AntonopoulosOutlineOptimizationProblemsIntroductionThe Class DPOracle ClassesThePolynomialHierarchyDefinitionBasic TheoremsBPP and PHDefinitionP NP[logn] is the class of all languages decided by a polynomialtime oracle machine, which on input x asks a total ofO(log |x|) SAT queries.FP NP[logn] is the corresponding class of functions.CLIQUE SIZE DefinitionGiven a graph, determine the size of his largest clique.TheoremCLIQUE SIZE is FP NP[logn] -complete.
ConclusionThePolynomialHierarchyA.AntonopoulosOutlineOptimizationProblemsIntroductionThe Class DPOracle ClassesThePolynomialHierarchyDefinitionBasic TheoremsBPP and PH1 TSP (D) is NP-complete.2 EXACT TSP is DP-complete.3 TSP COST is FP NP -complete.4 TSP is FP NP -complete.And now,P NP → NP NP ?Oracles for NP NP ?
Page 1 and 2: ThePolynomialHierarchyA.Antonopoulo
Page 4: DP Class DefinitionThePolynomialHie
Page 7 and 8: Complete Problems for DPThePolynomi
Page 9 and 10: Complete Problems for DPThePolynomi
Page 11 and 12: Other DP-complete problemsThePolyno
Page 13: FP NP -complete ProblemsThePolynomi
Page 16 and 17: FP NP -complete ProblemsThePolynomi
Page 24 and 25: NP[log n]The Class PThePolynomialHi
Page 28 and 29: OutlineThePolynomialHierarchyA.Anto
Page 30 and 31: The Polynomial HierarchyThePolynomi
Page 32 and 33: Basic TheoremsThePolynomialHierarch
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Page 47 and 48: BPP and PHThePolynomialHierarchyA.A

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