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MiniSAT: World fastest SAT solver (2005 and 2006)

MiniSAT: World fastest SAT solver (2005 and 2006). Niklas Sorensson, Niklas Een and Armin Biere Presenting: Tamir Heyman Some slides are from Niklas Sorensson presentation. DPLL SAT Solving. Branching Unit propagation Backtracking Learning. Learning in SAT Solver.

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MiniSAT: World fastest SAT solver (2005 and 2006)

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  1. MiniSAT: World fastest SAT solver (2005 and 2006) Niklas Sorensson, Niklas Een and Armin Biere Presenting: Tamir Heyman Some slides are from Niklas Sorensson presentation

  2. DPLL SAT Solving • Branching • Unit propagation • Backtracking • Learning

  3. Learning in SAT Solver • A conflict happens when one clause is falsified by unit propagation • Analyze the conflict to infer a clause • This clause is a logical consequence of the problem • The inferred clause is a new knowledge

  4. Conflict Clause • Inferred by conflict analysis • Helps prune future parts of the search space • Actually drives backtracking

  5. Conflict Clause Requirements • Consequence of the clause set • Falsified by current assignment • Contains exactly one literal implied by last assumption

  6. Conflict Analysis Algorithm • Begin with conflicting clause • Resolve on the most recently propagated literal • Using the antecedent as side clause • Repeat until the clause contains exactly one literal from the last assumption

  7. Example e=F a=T Conflict : b _:c _:d

  8. Example e=F a=T : b _:c _:d

  9. Example e=F a=T : b _:c _:d : b _:c _ h

  10. Example e=F a=T : b _:c _:d : b _:c_ h

  11. Example e=F a=T : b _:c _:d : b _:c _ h : b _ e _ f _ h

  12. Example e=F a=T b=F : b _:c _:d : b _:c _ h : b _ e _ f _ h

  13. Conflict Minimizing • Traditional Conflict Analysis is minimal in the number of derivations • Balance between time spent and usefulness of the conflict clause • Is a shorter clause always better?

  14. Basic Conflict Minimizing • Start from an ordinary conflict clause • Apply resolution greedily • Works because there are no cyclic dependencies • Also uses antecedent clauses from other levels • Very cheap, almost for free

  15. Example e=F a=T b=F : b _:c _:d : b _:c _ h : b _ e _ h Çf

  16. Example e=F a=T b=F : b _:c _:d : b _:c _ h : b _ e _ h Çf : b _ e Ç h

  17. TimeLine 1996 GRASP 1k var 1994 Hannibal  3k var 1960 DP 10 var 1988 SOCRATES  3k var 2005-6 Minisat 100k var 1996 SATO 1k var 1996 Stålmarck  1000 var 1962 DLL  10 var 1986 BDD  100 var 1992 GSAT  300 var 2001 Chaff 10k var

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