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(Created page with "{{DISPLAYTITLE: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), [...") |
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== Parameters == | == Parameters == | ||
$n$: number of variables | |||
== Table of Algorithms == | == Table of Algorithms == | ||
{| class="wikitable sortable" style="text-align:center;" width="100%" | |||
! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference | |||
|- | |||
| [[Davis-Putnam-Logemann-Loveland Algorithm (DPLL) (CNF-SAT Boolean Satisfiability)|Davis-Putnam-Logemann-Loveland Algorithm (DPLL)]] || 1961 || $O({2}^n)$ || $O(n)$ || Exact || Deterministic || [https://dl.acm.org/doi/10.1145/368273.368557 Time] & [https://en.wikipedia.org/wiki/DPLL_algorithm Space] | |||
|- | |||
| [[Conflict-Driven Clause Learning (CDCL) (CNF-SAT Boolean Satisfiability)|Conflict-Driven Clause Learning (CDCL)]] || 1999 || $O({2}^n)$ || || Exact || Deterministic || [https://ieeexplore.ieee.org/document/769433 Time] | |||
|- | |||
| [[GSAT (CNF-SAT Boolean Satisfiability)|GSAT]] || 1992 || $O(n*mt*mf)$ || $O(n)$ || || Randomized || [http://www.cs.cornell.edu/selman/papers/pdf/92.aaai.gsat.pdf Time] | |||
|- | |||
| [[WalkSAT (CNF-SAT Boolean Satisfiability)|WalkSAT]] || 1994 || $O(n*mt*mf)$ || $O(n)$ || || Randomized || [https://www.aaai.org/Papers/AAAI/1994/AAAI94-051.pdf Time] | |||
|- | |||
| [[Quantum Adiabatic Algorithm (QAA) (CNF-SAT Boolean Satisfiability)|Quantum Adiabatic Algorithm (QAA)]] || 2001 || $O({2}^n)$ || $O(poly(n)$) || || Quantum || [https://arxiv.org/pdf/quant-ph/0001106.pdf Time] | |||
|- | |||
| [[Paturi, Pudlák, Saks, Zane (PPSZ) 2005 (k-SAT Boolean Satisfiability)|Paturi, Pudlák, Saks, Zane (PPSZ)]] || 2005 || O^*({2}^{n-cn/k}) || $O(kn)$ || Exact || Randomized || [https://dl.acm.org/doi/abs/10.1145/1066100.1066101 Time] | |||
|- | |||
| [[Hertli (Modified PPSZ) (3SAT Boolean Satisfiability)|Hertli (Modified PPSZ)]] || 2014 || $O({1.30704}^n)$ || $O(kn)$ || Exact || Randomized || [https://epubs.siam.org/doi/abs/10.1137/120868177 Time] | |||
|- | |||
| [[Hertli (Modified PPSZ) (4SAT Boolean Satisfiability)|Hertli (Modified PPSZ)]] || 2014 || $O({1.46899}^n)$ || $O(kn)$ || Exact || Randomized || [https://epubs.siam.org/doi/abs/10.1137/120868177 Time] | |||
|- | |||
| [[Shi 2009 (NAE 3SAT Boolean Satisfiability)|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 || [https://ieeexplore.ieee.org/abstract/document/5211463 Time] & [https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5211463 Space] | |||
|- | |||
|} | |||
Latest revision as of 07:53, 10 April 2023
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 |