SAT (Boolean Satisfiability)

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