introduction what we know community structure and lbd
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introduction What we know Community Structure and LBD Conclusion S T solvers: why are they working so well? Laurent Simon Labri, Bordeaux, France some common work with Gilles Audemard CRIL, Lens, France George


  1.  introduction What we know Community Structure and LBD Conclusion S  T solvers: why are they working so well?  Laurent Simon  Labri, Bordeaux, France some common work with  Gilles Audemard  CRIL, Lens, France  George Katsirelos  INRA, Toulouse, France  (Beyond NP, Paris)  2017, May, 10th  1/41

  2.  introduction What we know Community Structure and LBD Conclusion Today’s Itinerary Introduction What we know Community Structure and LBD Conclusion  (Beyond NP, Paris)  2017, May, 10th  2/41

  3.  introduction What we know Community Structure and LBD Conclusion Today’s Itinerary Introduction  Preliminaries  DP-60  DPLL-62  SAT ingredients  Literal Block Distance and glucose What we know Community Structure and LBD Conclusion  (Beyond NP, Paris)  2017, May, 10th  3/41

  4. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2002  (Beyond NP, Paris)  2017, May, 10th  4/41

  5. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2003  (Beyond NP, Paris)  2017, May, 10th  4/41

  6. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2005  (Beyond NP, Paris)  2017, May, 10th  4/41

  7. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2007  (Beyond NP, Paris)  2017, May, 10th  4/41

  8. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2009  (Beyond NP, Paris)  2017, May, 10th  4/41

  9. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2011  (Beyond NP, Paris)  2017, May, 10th  4/41

  10. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2014  (Beyond NP, Paris)  2017, May, 10th  4/41

  11. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� � ���� ������� � ������� � ���� � ��������� � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� 2016  (Beyond NP, Paris)  2017, May, 10th  4/41

  12. introduction What we know Community Structure and LBD Conclusion Performances of SAT Solvers, after 2001 � ���� ���������� � ������ �������� � ������ �������������� � ������ ������� � ������ �������� � ������ ������� � ������ � ���� ������������� � ������ ������� � ������ ���������������� � ������ ������� � ������� � ���� � ��������� ������������������� � ������ � ���� � ���� � ��� � � � �� � �� � �� � ��� � ��� � ��� � ��� � ��� � ��� � ��� ������ � �� � ������ � �������� � ����� � ��� � ��� � ������ � ���� � ����� the winners  (Beyond NP, Paris)  2017, May, 10th  4/41

  13. introduction What we know Community Structure and LBD Conclusion The firsts SAT steps 1958 : Hilary Putnam and Martin Davis look for funding their research around propositional logic « What we’re interested in is good algorithms for propositional calculus » (NSA) Before that , only inefficient methods (truth tables, . . . ) First papers Computational Methods in The Propositional calculus [Davis Putnam 1958] 1 A Computing Procedure for Quantification Theory [Davis Putnam 1960] 1 Rapport interne NSA  (Beyond NP, Paris)  2017, May, 10th  5/41

  14. introduction What we know Community Structure and LBD Conclusion 1960, already a first (kind of) competition! « The superiority of the present procedure (i.e. DP) over those previously available is indicated in part by the fact that a formula on which Gilmores routine for the IBM 704 causes the machine to compute for 21 minutes without obtaining a result was worked successfully by hand computation using the present method in 30 minutes » [Davis et Putnam 1960], page 202. One of the reasons of the success of SAT is its competitions  (Beyond NP, Paris)  2017, May, 10th  6/41

  15. introduction What we know Community Structure and LBD Conclusion Principles of DP-60 DP-60: forgets variables one after the other Example : forgets x 1 . x 1 ∨ x 4 x 1 ∨ x 4 ∨ x 14 x 1 ∨ x 3 ∨ x 8 x 1 ∨ x 8 ∨ x 12 x 1 ∨ x 5 ∨ x 9 x 2 ∨ x 11 x 3 ∨ x 7 ∨ x 13 x 3 ∨ x 7 ∨ x 13 ∨ x 9 x 8 ∨ x 7 ∨ x 9  (Beyond NP, Paris)  2017, May, 10th  7/41

  16. introduction What we know Community Structure and LBD Conclusion Principles of DP-60 DP-60: forgets variables one after the other Example : forgets x 1 . x 1 ∨ x 4 x 1 ∨ x 8 ∨ x 12 x 1 ∨ x 5 ∨ x 9 x 1 ∨ x 4 ∨ x 14 x 1 ∨ x 3 ∨ x 8 x 2 ∨ x 11 x 3 ∨ x 7 ∨ x 13 x 3 ∨ x 7 ∨ x 13 ∨ x 9 x 8 ∨ x 7 ∨ x 9  (Beyond NP, Paris)  2017, May, 10th  7/41

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