Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-12-14 , DOI: 10.1016/j.tcs.2020.12.021 Kristóf Bérczi , Endre Boros , Ondřej Čepek , Khaled Elbassioni , Petr Kučera , Kazuhisa Makino
Given a CNF formula Φ with clauses and variables , a truth assignment of Φ leads to a clause sequence where if clause evaluates to 1 under assignment a, otherwise . The set of all possible clause sequences carries a lot of information on the formula, e.g. SAT, MAX-SAT and MIN-SAT can be encoded in terms of finding a clause sequence with extremal properties.
We consider a problem posed at Dagstuhl Seminar 19211 “Enumeration in Data Management” (2019) about the generation of all possible clause sequences of a given CNF with bounded dimension. We prove that the problem can be solved in incremental polynomial time. We further give an algorithm with polynomial delay for the class of tractable CNF formulas. We also consider the generation of maximal and minimal clause sequences, and show that generating maximal clause sequences is NP-hard, while minimal clause sequences can be generated with polynomial delay.
中文翻译:
生成CNF公式的子句序列
给定具有子句的CNF公式Φ 和变量 ,真相分配 Φ导致子句序列 哪里 if子句 在分配a下求值为1 ,否则为。所有可能的子句序列的集合都包含大量有关公式的信息,例如SAT,MAX-SAT和MIN-SAT可以根据找到具有极性质的子句序列进行编码。
我们考虑在Dagstuhl研讨会19211“数据管理中的枚举”(2019)中提出的问题,该问题涉及给定CNF的有限维的所有可能子句序列的生成。我们证明该问题可以在增量多项式时间内解决。对于可处理的CNF公式,我们进一步给出了具有多项式延迟的算法。我们还考虑了最大子句序列和最小子句序列的生成,并表明生成最大子句序列是NP-hard的,而最小子句序列可以通过多项式延迟生成。