Lecture 4 : More NP - completeness , NP - search , coNP
نویسنده
چکیده
We first observe that NP-completeness immediately follows forCNFSAT and SAT since 3SAT ≤p CNFSAT ≤p SAT . Note that 3SAT ⊂ CNFSAT ⊂ SAT . The reduction in each case is almost the identity (though of course it can’t be since the sets are different). The only issue is that we have to modify satisfiable formulas that are not in 3CNF. For the 3SAT ≤p CNFSAT reduction we simply map any input that is not in 3CNF to some fixed object like x ∧ ¬x and so the same for the CNFSAT ≤p SAT reduction for formulas not in CNF.
منابع مشابه
INFR 11102 : Computational Complexity 13 / 02 / 2018 Lecture 9 : Polynomial hierarchy
1.1 coNP Recall that by L we denote the complement language of L, namely x ∈ L if and only if x ̸∈ L. Define coNP = {L | L ∈ NP}. Similar to NP, there is an alternative definition of coNP. Definition 1. A language L is in coNP if there is a polynomial p(·) and a polynomial-time TM M such that x ∈ L ⇔ ∀y, |y| ≤ p(|x|), M(x, y) = 1. Recall that in the alternative definition of NP, a certificate y ...
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