k-SAT (Boolean Satisfiability)

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k-SAT restricts the boolean formula to CNF with (at most) k literals per clause

Related Problems

Generalizations: Conjunctive Normal Form SAT

Subproblem: 2SAT, 3SAT, 4SAT

Related: SAT, Disjunctive Normal Form SAT, 1-in-3SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal 3-SAT (NAE 3SAT), Monotone Not-All-Equal 3-SAT (Monotone NAE 3SAT), 3SAT, 3SAT-5, 4SAT, Monotone 3SAT, XOR-SAT, Horn SAT, Dual-Horn SAT, Renamable Horn, MaxSAT


$n$: number of variables

$k$: max number of literals per clause

$c$: dependant on $k$

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Paturi, Pudlák, Saks, Zane (PPSZ) 2005 O^*({2}^{n-cn/k}) $O(kn)$ Exact Randomized Time

Reductions TO Problem

Problem Implication Year Citation Reduction
Subset Sum assume: SETH
then: for any $\epsilon > {0}$ there exists a $\delta > {0}$ such that Subset Sum is not in time $O(T^{1-\epsilon}{2}^{\delta n})$, and $k$-Sum is not in time $O(T^{1-\epsilon}n^{\delta k})$
2022 https://dl.acm.org/doi/full/10.1145/3450524 link