SAT (Boolean Satisfiability)
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Description
Boolean satisfiability problems involve determining if there is an assignment of variables that satisfies a given boolean formula.
Related Problems
Subproblem: Conjunctive Normal Form SAT, Disjunctive Normal Form SAT
Related: 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), k-SAT, 2SAT, 3SAT, 3SAT-5, 4SAT, Monotone 3SAT, XOR-SAT, Horn SAT, Dual-Horn SAT, Renamable Horn, MaxSAT
Parameters
$n$: number of variables
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Davis-Putnam-Logemann-Loveland Algorithm (DPLL) | 1961 | $O({2}^n)$ | $O(n)$ | Exact | Deterministic | Time & Space |
| Conflict-Driven Clause Learning (CDCL) | 1999 | $O({2}^n)$ | Exact | Deterministic | Time | |
| GSAT | 1992 | $O(n*mt*mf)$ | $O(n)$ | Randomized | Time | |
| WalkSAT | 1994 | $O(n*mt*mf)$ | $O(n)$ | Randomized | Time | |
| Quantum Adiabatic Algorithm (QAA) | 2001 | $O({2}^n)$ | $O(poly(n)$) | Quantum | Time | |
| Paturi, Pudlák, Saks, Zane (PPSZ) | 2005 | O^*({2}^{n-cn/k}) | $O(kn)$ | Exact | Randomized | Time |
| Hertli (Modified PPSZ) | 2014 | $O({1.30704}^n)$ | $O(kn)$ | Exact | Randomized | Time |
| Hertli (Modified PPSZ) | 2014 | $O({1.46899}^n)$ | $O(kn)$ | Exact | Randomized | Time |
| Shi | 2009 | $O({12}m*t_extract + {2}m*t_discard + {2}n*t_append + (n+{2}m)$*t_merge + (n-{1})*t_amplify) | $O(n)$ tubes or $O({2}^n)$ library strands | Exact | Deterministic | Time & Space |