題目
8.8 In the EXACT 4SAT problem, the input is a set of clauses, each of which is a disjunction of exactly four literals, and such that each variable occurs at most once in each clause. The goal is to find a satisfying
assignment, if one exists. Prove that EXACT 4SET is NP-complete.
解答
可以將3SAT歸約爲EXACT 4SAT，對於任意一個3SAT，若其中某子串中一個文字多次出現，則可以減爲一次；如果某變量的肯定和否定同時出現，則可去掉該變量；可以在添加輔助變量，如上將子串中的字符數擴充至4，3SAT歸約爲EXACT 4SAT問題，EXACT 4SAT問題屬於NP難。
