## On Computing Minimum Unsatisfiable Cores (2003)

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Citations: | 31 - 3 self |

### BibTeX

@MISC{Lynce03oncomputing,

author = {I. Lynce and J. Marques-Silva},

title = {On Computing Minimum Unsatisfiable Cores},

year = {2003}

}

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### Abstract

Certifying the correctness of a SAT solver is straightforward for satisfiable instances of SAT. Given a

### Citations

1114 | Chaff: Engineering an efficient SAT solver - Moskewicz, Madigan, et al. - 2001 |

1075 | A computing procedure for quantification theory - Davis, Putnam - 1960 |

577 | Where the really hard problems are
- Cheeseman, Kanefsky, et al.
- 1991
(Show Context)
Citation Context ...est value found by the time the search finishes may already represent a significant reduction to the size of the unsatisfiable core given by zChaff. Table 2 gives results for selected uuf50 instances =-=[4]-=-. These results are representative of the results obtained for the whole benchmark family. It is clear that the initial core may indeed be reduced, even though the best value found in 3600s is not pro... |

529 | A machine program for theorem-proving - Davis, Logemann, et al. - 1962 |

359 | GRASP a new search algorithm for satisfiability
- Marques-Silva, Sakallah
- 1996
(Show Context)
Citation Context ...is unsatisfiable if it is possible to generate an empty clause by resolution from the original clauses. This approaches basically extracts unsatisfiable cores based on the conflict analysis procedure =-=[9]-=-. The unsatisfiable core is given by the set of original clauses involved in the derivation of the empty clause. Recent work by Oh et al. [12] proposes extracting a minimal unsatisfiable core. The fir... |

239 | BerkMin: a Fast and Robust Sat-Solver - Goldberg, Novikov - 2002 |

195 | Interpolation and SAT-Based Model Checking
- McMillan
- 2003
(Show Context)
Citation Context ...he minimum unsatisfiable core). Besides the theoretical interest of computing unsatisfiable cores, or minimum unsatisfiable cores, the recent utilization of SAT technology in Unbounded Model Checking =-=[11]-=- also relies extensively on the ability of SAT solvers for generating proofs of unsatisfiability and for computing unsatisfiable cores. As a result, the utilization of SAT solvers in Model Checking re... |

156 | Using CSP look-back techniques to solve real-world SAT instances - Schrag - 1997 |

108 | Automatic Abstraction without Counterexamples - McMillan, Amla - 2003 |

100 | Validating SAT solvers using an independent resolutionbased checker: Practical implementations and other applications
- Zhang, Malik
- 2003
(Show Context)
Citation Context ...cial for correcting the minimum amount of inconsistent information (e.g. in knowledge bases). 1 Introduction The utilization of SAT in industrial settings has motivated work on certifying SAT solvers =-=[14]-=-. Given a problem instance, the certifier needs to be able to verify that the computed truth assignments indeed satisfy a satisfiable instance and that, for an unsatisfiable instance, a proof of unsat... |

68 | Quickxplain: Conflict detection for arbitrary constraint propagation algorithms
- Junker
- 2001
(Show Context)
Citation Context ... interactive applications requiring explanations. For this domain it is crucial identifying precisely why a set of constraints is inconsistent and to correct it with the least number of modifications =-=[8]-=-. The paper is organized as follows. The next section surveys the work on computing unsatisfiable cores. This motivates the question of how to compute the minimum unsatisfiable core, and section 3 pro... |

44 |
The complexity of facets resolved
- Papadimitriou, Wolfe
- 1988
(Show Context)
Citation Context ...ores. Research work can be distinguished between theoretical and experimental work. In the theoretical field, unsatisfiable cores complexity has been analyzed and formal algorithms have been proposed =-=[3, 5, 6, 13]-=-. Experimental work includes contributions of Bruni and Sassamo [2] and Zhang and Malik [14] 1 . Both approaches extract unsatisfiable cores. The first proposes an adaptative search guided by clauses ... |

41 | Verification of proofs of unsatisfiability for CNF formulas
- Goldberg
(Show Context)
Citation Context ... ¬x2 ∨ x3 ω5 = x2 ∨ x3 ω2 = x2 ω4 = ¬x2 ∨ ¬x3 ω6 = ¬x1 ∨ x2 ∨ ¬x3 From the formula ϕ above, we can identify nine different unsatisfiable cores UC1, ..., UC9: 1 A similar approach has been proposed in =-=[7]-=-. Basically, in [14] the information required is recorded during the search, whereas in [7] it is computed after the search.sOn Computing Minimum Unsatisfiable Cores 307 UC1 = {ω1, ω2, ω3, ω4, ω5, ω6}... |

39 |
Boosting complete techniques thanks to local search methods
- Mazure, Gregoire
(Show Context)
Citation Context ...ere the identification of a subset with the minimum number of clauses may be crucial. Observe that repairing inconsistent knowledge in real-world applications is a quite often problem to be addressed =-=[10]-=-, although to the extent of our knowledge the identification of the minimum inconsistent kernel has never been addressed. Another application domain is interactive applications requiring explanations.... |

35 | Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
- Fleischner, Kullman, et al.
(Show Context)
Citation Context ...ores. Research work can be distinguished between theoretical and experimental work. In the theoretical field, unsatisfiable cores complexity has been analyzed and formal algorithms have been proposed =-=[3, 5, 6, 13]-=-. Experimental work includes contributions of Bruni and Sassamo [2] and Zhang and Malik [14] 1 . Both approaches extract unsatisfiable cores. The first proposes an adaptative search guided by clauses ... |

34 |
Buning: An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF
- Davydov, Davydova, et al.
- 1998
(Show Context)
Citation Context ...ores. Research work can be distinguished between theoretical and experimental work. In the theoretical field, unsatisfiable cores complexity has been analyzed and formal algorithms have been proposed =-=[3, 5, 6, 13]-=-. Experimental work includes contributions of Bruni and Sassamo [2] and Zhang and Malik [14] 1 . Both approaches extract unsatisfiable cores. The first proposes an adaptative search guided by clauses ... |

32 |
Random generation of test instances with controlled attributes
- ASAHIRO, IWAMA, et al.
- 1996
(Show Context)
Citation Context ... the number of S variables to be assigned value 1. During the search, the bound decreases whenever a new smaller unsatisfiable core is found. 6 We used the aim generator for obtaining these instances =-=[1]-=-.s310 Inês Lynce and João Marques-Silva the minimum unsatisfiable core. Consequently, it is indeed useful to use this tool with the goal of reducing the minimal unsatisfiable core given by zChaff. 5 C... |

32 | AMUSE: a minimally-unsatisfiable subformula extractor
- Oh, Mneimneh, et al.
- 2004
(Show Context)
Citation Context ...satisfiable cores based on the conflict analysis procedure [9]. The unsatisfiable core is given by the set of original clauses involved in the derivation of the empty clause. Recent work by Oh et al. =-=[12]-=- proposes extracting a minimal unsatisfiable core. The first step for computing an unsatisfiable core consists in identifying the clauses (either original or recorded) that were involved in the steps ... |

27 | Restoring Satisfiability or Maintaining Unsatisfiability by finding small Unsatisfiable Subformulae
- Bruni, Sassano
(Show Context)
Citation Context ... work. In the theoretical field, unsatisfiable cores complexity has been analyzed and formal algorithms have been proposed [3, 5, 6, 13]. Experimental work includes contributions of Bruni and Sassamo =-=[2]-=- and Zhang and Malik [14] 1 . Both approaches extract unsatisfiable cores. The first proposes an adaptative search guided by clauses hardness. The second approach is motivated by considering that a CN... |

9 | On subclasses of minimal unsatisfiable formulas
- Büning
(Show Context)
Citation Context |