2020/02/17 by Kristóf Bérczi, Bérczi, Kristóf, Endre Boros +9
Computer Science · #Algorithms and Data Compression #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Machine Learning and Algorithms #semigroups and automata theory
paper · doi:10.48550/arxiv.2002.06727
openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a CNF formula Φ with clauses C1,…,Cm and variables V=\x1,…,xn\, a truth assignment a:V→\0,1\ of Φ leads to a clause sequence σΦ(a)=(C1(a),…,Cm(a))∈\0,1\m where Ci(a) = 1 if clause Ci evaluates to 1 under assignment a, otherwise Ci(a) = 0. 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.