## Efficient Data Structures for Backtrack Search SAT Solvers (2002)

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Citations: | 22 - 3 self |

### BibTeX

@MISC{Lynce02efficientdata,

author = {Ines Lynce and Joao Marquez-Silva},

title = {Efficient Data Structures for Backtrack Search SAT Solvers},

year = {2002}

}

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### Abstract

The implementation of efficient Propositional Satisfiability (SAT) solvers entails the utilization of highly efficient data structures, as illustrated by most of the recent state-of-the-art SAT solvers. However, it is in general hard to compare existing data structures, since different solvers are often characterized by fairly different algorithmic organizations and techniques, and by different search strategies and heuristics. This paper aims the evaluation of data structures for backtrack search SAT solvers, under a common unbiased SAT framework. In addition, advantages and drawbacks of each existing data structure are identified. Finally, new data structures are proposed, that are competitive with the most efficient data structures currently available, and that may be preferable for the next generation SAT solvers.

### Citations

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(Show Context)
Citation Context ...of the clauses of CNF formula ϕ. In the following sections we shall address backtrack search algorithms for SAT. Most if not all backtrack search SAT algorithms apply extensively the unit clause rule =-=[6]-=-. If a clause is unit, then the sole free literal must be assigned value 1 for the formula to be satisfiable. In this case, the value of the literal and of the associated variable are said to be impli... |

530 |
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(Show Context)
Citation Context ...e obtained in recent years [2,12,14]. 3.1. General organization The vast majority of backtrack search SAT algorithms build upon the original backtrack search algorithm of Davis, Logemann and Loveland =-=[5]-=-. Most backtrack search SAT solvers are conceptually composed of three main stages: 1. The decision stage elects the variable and value to assign at each branching step of the search process. 2. The d... |

314 | Boosting combinatorial search through randomization
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(Show Context)
Citation Context ...d using clause recording and non-chronological backtracking in SAT solvers. More recently, search restart strategies have been shown to be extremely effective for solving real-world problem instances =-=[2,8]-=-. Finally, the most recent paradigm shift was observed first in SATO [18] and more recently and more drastically in Chaff [14], that proposed several significant new ideas on how to efficiently implem... |

215 | Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems - Selman, Kautz - 1993 |

157 |
Using CSP lookback techniques to solve real-world SAT instances
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(Show Context)
Citation Context ... new search strategies, new search techniques and new implementations. Broadly, improvements in SAT solvers have been characterized by a few significant paradigm shifts. First, GRASP [12] and rel-sat =-=[3]-=- very successfully proposed using clause recording and non-chronological backtracking in SAT solvers. More recently, search restart strategies have been shown to be extremely effective for solving rea... |

66 |
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(Show Context)
Citation Context ...se ω becomes satisfied, ω is hidden from the list of clauses of all the variables with literals in ω. The technique of hiding satisfied clauses can be traced back to the work of O. Coudert in Scherzo =-=[4]-=- for the Binate Covering Problem. The motivation for hiding clauses is to reduce the amount of work required each time a variable x is assigned, since in this case only the unresolved clauses associat... |

57 | A computing procedure for quanti theory - Davis, Putnam - 1960 |

54 | Using randomization and learning to solve hard real-world instances of satisfiability
- Baptista, Marques-Silva
(Show Context)
Citation Context ...d using clause recording and non-chronological backtracking in SAT solvers. More recently, search restart strategies have been shown to be extremely effective for solving real-world problem instances =-=[2,8]-=-. Finally, the most recent paradigm shift was observed first in SATO [18] and more recently and more drastically in Chaff [14], that proposed several significant new ideas on how to efficiently implem... |

53 | Cha#: Engineering an e#cient sat solver - Moskewicz, Madigan, et al. - 2001 |

41 | The propositional formula checker heerhugo
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(Show Context)
Citation Context ...ch SAT algorithms include identification of unique implication points [12] and relevance-based learning [3]. (We should observe that a number of other techniques is often used as a preprocessing step =-=[7,9]-=-.) 3.4. Implementation paradigms Implementation issues for SAT solvers include the design of suitable data structures for storing variables, clauses and literals. The elected data structures dictate t... |

39 | SATO: An ecient propositional prover - Zhang - 1997 |

22 | GRASP: A new search algorithm for satis - Marques-Silva, Sakallah - 1996 |

19 | Stochastic systematic search algorithms for satisfiability - Lynce, Baptista, et al. - 2001 |

19 | Algebraic simplification techniques for propositional satisfiability
- Marques-Silva
- 2000
(Show Context)
Citation Context ...nary and ternary clauses) [1,9,13]. Even though some of these techniques are often used as a preprocessing step by SAT solvers, their application during the search phase has been proposed in the past =-=[11,13]-=-. The objective of this section is thus to measure the laziness of lazy data structures during the search process. The more lazy a (lazy) data structure is, the less suitable it is for implementing (l... |

16 | Exploiting the computational tradeoff of more reasoning and less searching
- Bacchus
- 2002
(Show Context)
Citation Context ...quivalence conditions (from pairs of binary clauses), restricted resolution (between binary and ternary clauses), and pattern-based clause inference conditions (also using binary and ternary clauses) =-=[1,9,13]-=-. Even though some of these techniques are often used as a preprocessing step by SAT solvers, their application during the search phase has been proposed in the past [11,13]. The objective of this sec... |

11 |
Satisfiability testing with more reasoning and less guessing
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(Show Context)
Citation Context ...ch SAT algorithms include identification of unique implication points [12] and relevance-based learning [3]. (We should observe that a number of other techniques is often used as a preprocessing step =-=[7,9]-=-.) 3.4. Implementation paradigms Implementation issues for SAT solvers include the design of suitable data structures for storing variables, clauses and literals. The elected data structures dictate t... |

8 | Algebraic simpli techniques for propositional satis - Marques-Silva - 2000 |

5 | Li and Anbulagan. Look-ahead versus lookback for satis problems - M - 1997 |

4 |
versus Look-Back for Satisfiability Problems
- Li, Anbulagan
- 1997
(Show Context)
Citation Context ...T solvers 139 3. Backtrack search algorithms Over the years a large number of algorithms has been proposed for SAT, from the original Davis–Putnam procedure [6], to recent backtrack search algorithms =-=[3,10,12, 14,17]-=-, to local search algorithms [15], among many others. SAT algorithms can be characterized as being either complete or incomplete. Complete algorithms can establish unsatisfiability if given enough CPU... |