Lecture 15 : Unique - SAT , Toda ’ s Theorem , Circuit Lower
نویسنده
چکیده
Definition 1.1. Let USAT ⊆ SAT be the set of formulas φ such that φ has a unique satisfying assignment. Let UP be the set of languages A such that there is a polytime TM M and a polynomial p such that x ∈ A⇔ ∃!y ∈ {0, 1}p(|x|) (M(x, y) = 1). Lemma 1.2 (Valiant-Vazirani). There is a randomized polynomial-computable reduction f from SAT to USAT with the following properties: [φ] ∈ SAT → [f(φ)] ∈ USAT ] ≥ 1/(8n) [φ] / ∈ SAT → [f(φ)] ∈ SAT ] = 0.
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