## Efficient Conflict Driven Learning in a Boolean Satisfiability Solver (2001)

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Venue: | In ICCAD |

Citations: | 295 - 8 self |

### BibTeX

@INPROCEEDINGS{Zhang01efficientconflict,

author = {Lintao Zhang and Conor F. Madigan and Matthew H. Moskewicz},

title = {Efficient Conflict Driven Learning in a Boolean Satisfiability Solver},

booktitle = {In ICCAD},

year = {2001},

pages = {279--285}

}

### Years of Citing Articles

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### Abstract

One of the most important features of current state-of-the-art SAT solvers is the use of conflict based backtracking and learning techniques. In this paper, we generalize various conflict driven learning strategies in terms of different partitioning schemes of the implication graph. We re-examine the learning techniques used in various SAT solvers and propose an array of new learning schemes. Extensive experiments with real world examples show that the best performing new learning scheme has at least a 2X speedup compared with learning schemes employed in state-of-the-art SAT solvers.

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Citation Context ... Here V and E are the number of vertices and edges of the implication graph respectively. The time complexity for finding a min-cut of the implication graph can be implemented in O(VElg(V 2 /E)) time =-=[17]-=-. A good learning scheme should reduce the number of decisions needed to solve certain problems as much as possible. The effectiveness of a learning scheme is very hard to determine a priori. Generall... |

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Citation Context ... assignment exists. Various EDA applications ranging from formal verification [2][3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP =-=[6], P-=-OSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorithm [11]) have been proposed to solve the SAT proble... |

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Citation Context ...nging from formal verification [2][3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat =-=[4], C-=-haff [9]) based on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorithm [11]) have been proposed to solve the SAT problem efficiently for practical problem instances. ... |

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Citation Context ...enerally not help searches in other parts. More advanced conflict analysis relies on the implication graph to determine the actual reasons for the conflict. This kind of conflict directed backjumping =-=[7]-=- could back up more than one level of the decision stack. Thus, it is also called nonchronological backtracking. At the same time, the conflict analysis engine will also add some clauses to the databa... |

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Citation Context ... exists. Various EDA applications ranging from formal verification [2][3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT =-=[5], S-=-ATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorithm [11]) have been proposed to solve the SAT problem efficient... |

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Citation Context ...ere are a large number of different SAT solvers that differ mainly in how each of these functions is implemented using different heuristics. A lot of effort has been spent on decisionmaking (e.g. [13]=-=[14]-=-[9]), and significant progress has been made on how efficient deduction (e.g. [9][15][8]). However, to our knowledge, only [7] and [6] (and its variations) have discussed implementation of conflict dr... |

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Citation Context ... asks for an assignment of variables so that the formula evaluates to true, or a determination that no such assignment exists. Various EDA applications ranging from formal verification [2][3] to ATPG =-=[1]-=- use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algorithms (e.g.... |

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Citation Context ... SAT problem asks for an assignment of variables so that the formula evaluates to true, or a determination that no such assignment exists. Various EDA applications ranging from formal verification [2]=-=[3]-=- to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algo... |

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Citation Context .... There are a large number of different SAT solvers that differ mainly in how each of these functions is implemented using different heuristics. A lot of effort has been spent on decisionmaking (e.g. =-=[13]-=-[14][9]), and significant progress has been made on how efficient deduction (e.g. [9][15][8]). However, to our knowledge, only [7] and [6] (and its variations) have discussed implementation of conflic... |

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Citation Context ...formal verification [2][3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff =-=[9]) b-=-ased on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorithm [11]) have been proposed to solve the SAT problem efficiently for practical problem instances. Most often,... |

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Citation Context ...the SAT problem asks for an assignment of variables so that the formula evaluates to true, or a determination that no such assignment exists. Various EDA applications ranging from formal verification =-=[2]-=-[3] to ATPG [1] use efficient SAT solvers as the basis for reasoning and searching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various a... |

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Citation Context ...earching. Many dedicated solvers (e.g. GRASP [6], POSIT [5], SATO [8], rel_sat [7], Walksat [4], Chaff [9]) based on various algorithms (e.g. Davis Putnam [10], local search [4], Stälmark’s algorit=-=hm [11]-=-) have been proposed to solve the SAT problem efficiently for practical problem instances. Most often, the Boolean formulae of SAT problems are expressed in Conjunctive Normal Form (CNF). A CNF formul... |

1 |
Chaff: A Fast SAT Solver for EDA
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- 2001
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Citation Context ...to difficult search regions because of bad decisions in the early decision stages. Random restarting periodically undoes all the decisions and restarts the search from the very beginning. As noted in =-=[12]-=-, frequent restarting actually does not hurt the solving process even for the unsatisfiable instances. The knowledge of the searched space is already recorded in the learned clauses. Therefore, discar... |

1 |
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Citation Context ... no good to include all the decision variables of the current search tree in the conflict clause, because such a combination of decisionssDecision Strategy S D I S V Microprocessor Formal Verification=-=[19]-=- Bounded Model Checking [18] fvp-unsat.1.0(4) sss.1.0(48) sss.1.0a(9) barrel (8) longmult(16) queueinvar(10) satplan(20) 1uip 532.8 24.56 10.63 1012.62 2887.11 6.58 39.34 2uip 746.87 27.32 16.96 641.6... |