Advanced Discrete Mathematics & Math
Q89 / 100

What is the polynomial hierarchy in descriptive complexity?

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The correct answer is B) Fagin's theorem: NP = ∃SO (properties expressible in existential second-order logic over ordered structures) — founding result of descriptive complexity

B

Correct Answer

Fagin's theorem: NP = ∃SO (properties expressible in existential second-order logic over ordered structures) — founding result of descriptive complexity

Explanation

Fagin (1974): NP = ∃SO on ordered finite structures. Immerman: P = FO+LFP (first-order logic + least fixpoint). This gives machine-independent characterizations: complexity classes are exactly certain logics.

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