[算法概论习题] 证明 EXACT 4SAT 是 NP-complete 问题

8.8. In the EXACT 4 SAT 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 4 SAT is NP-complete.

证明： 易证 EXACT 4SAT 问题是 NP 问题。已知，3SAT 问题为 NP-complete 问题，现将 3SAT 问题归约到 EXACT 4SAT，即可证明 EXACT 4SAT 为 NP-complete 问题。

对于一个 3SAT 问题，

(x¯∨y∨z¯)(x∨y¯∨