题目
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
可以将3SAT归约为EXACT 4SAT，对于任意一个3SAT，若其中某子串中一个文字多次出现，则可以减为一次；如果某变量的肯定和否定同时出现，则可去掉该变量；可以在添加辅助变量，如上将子串中的字符数扩充至4，3SAT归约为EXACT 4SAT问题，EXACT 4SAT问题属于NP难。