## Symbolic Decision Procedures for QBF (2004)

Venue: | Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004 |

Citations: | 24 - 1 self |

### BibTeX

@INPROCEEDINGS{Pan04symbolicdecision,

author = {Guoqiang Pan and Moshe Y. Vardi},

title = {Symbolic Decision Procedures for QBF},

booktitle = {Proceedings of 10th Int. Conf. on Principles and Practice of Constraint Programming (CP 2004},

year = {2004},

pages = {453--467},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

Much recent work has gone into adapting techniques that were originally developed for SAT solving to QBF solving. In particular, QBF solvers are often based on SAT solvers. Most competitive QBF solvers are search-based. In this work we explore an alternative approach to QBF solving, based on symbolic quantifier elimination. We extend some recent symbolic approaches for SAT solving to symbolic QBF solving, using various decision-diagram formalisms such as OBDDs and ZDDs. In both approaches, QBF formulas are solved by eliminating all their quantifiers. Our first solver, QMRES, maintains a set of clauses represented by a ZDD and eliminates quantifiers via multi-resolution. Our second solver, QBDD, maintains a set of OBDDs, and eliminate quantifier by applying them to the underlying OBDDs. We compare our symbolic solvers to several competitive search-based solvers. We show that QBDD is not competitive, but QMRES compares favorably with search-based solvers on various benchmarks consisting of non-random formulas.

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Citation Context ...iques that were originally developed for SAT solving to QBF solving, cf. [9, 41]. In particular, QBF solvers are often based on SAT solvers; for example, QuBE [31] is based on SIM [30], while Quaffle =-=[58]-=- is based on ZChaff [57]. Essentially all competitive QBF solvers are search-based [40]. In spite of the growing sophistication of QBF solvers, it is fair to say that they have shown nowhere near the ... |

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Citation Context ...e.) In [13] it is shown how zero-suppressed decision diagrams (ZDDs) [42] can offer a compact representation for sets of clauses and can support symbolic resolution (called there multiresolution). In =-=[47, 50]-=- it is shown how ordered Boolean decision diagrams (OBDDs) can support symbolic quantifier elimination. In both [13] and [47] the symbolic approach is compared to search-based approaches, showing that... |

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Citation Context ...rticular, QBF solvers are often based on SAT solvers; for example, QuBE [31] is based on SIM [30], while Quaffle [58] is based on ZChaff [57]. Essentially all competitive QBF solvers are search-based =-=[40]-=-. In spite of the growing sophistication of QBF solvers, it is fair to say that they have shown nowhere near the effectiveness of SAT solvers [40]. �Supported in part by NSF grants CCR-9988322, CCR-01... |

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Citation Context ...hod, which we describe as symbolic quantifier elimination, eliminates all quantifiers until we are left with the constant OBDD or . Symbolic quantifier elimination was first applied to SAT solving in =-=[33]-=- (under the name of hiding functions) and tried on random 3-SAT instances. The work in [50, 47] studied this method further, and considered various optimizations. 2 So far we processed the clauses of ... |

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