3SAT: Difference between revisions
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(Created page with "{{DISPLAYTITLE:3SAT (Boolean Satisfiability)}} == Description == 3SAT restricts the boolean formula to CNF with (at most) 3 literals per clause == Related Problems == Generalizations: k-SAT Subproblem: 1-in-3SAT, Not-All-Equal 3-SAT (NAE 3SAT), 3SAT-5, Monotone 3SAT Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, Monotone 1-in-3SAT, Monotone Not-Exactly-1-in-3SAT, All-Equal-SAT, Not-All-Equal...") |
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== Parameters == | == Parameters == | ||
$n$: number of variables | |||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Hertli (Modified PPSZ) (3SAT Boolean Satisfiability)|Hertli (Modified PPSZ)]] || 2014 || $O({1.30704}^n)$ || $O(kn)$ || Exact || Randomized || [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/abs/10.1137/120868177 Time] | | [[Hertli (Modified PPSZ) (3SAT Boolean Satisfiability)|Hertli (Modified PPSZ)]] || 2014 || $O({1.30704}^n)$ || $O(kn)$ || Exact || Randomized || [https://epubs-siam-org.ezproxy.canberra.edu.au/doi/abs/10.1137/120868177 Time] | ||
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| [[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.ezproxy.canberra.edu.au/abstract/document/5211463 Time] & [https://ieeexplore-ieee-org.ezproxy.canberra.edu.au/stamp/stamp.jsp?tp=&arnumber=5211463 Space] | |||
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Latest revision as of 08:53, 10 April 2023
Description
3SAT restricts the boolean formula to CNF with (at most) 3 literals per clause
Related Problems
Generalizations: k-SAT
Subproblem: 1-in-3SAT, Not-All-Equal 3-SAT (NAE 3SAT), 3SAT-5, Monotone 3SAT
Related: SAT, Conjunctive Normal Form SAT, Disjunctive Normal Form SAT, 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), 2SAT, 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 |
|---|---|---|---|---|---|---|
| Hertli (Modified PPSZ) | 2014 | $O({1.30704}^n)$ | $O(kn)$ | 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 |