Backdoor Sets of Quantified Boolean Formulas

Quantified constraint satisfaction problems (QCSPs) are an extension to constraint satisfaction problems (CSPs) with both universal quantifiers and existential quantifiers. In this paper we apply variable ordering heuristics and integrate standard dependency schemes in QCSP solvers. The technique can help to decide the next variable to be assigned in QCSP solving. We also introduce a new factor into the variable ordering heuristics: a variable's dep is the number of variables depending on it. This factor represents the probability of getting more candidates for the next variable to be assigned. Experimental results show that variable ordering heuristics with standard dependency schemes and the new factor dep can improve the performance of QCSP solvers.

show abstract

“…To compute standard dependency schemes we use methods similar to those in [12][13]15]. For a universal variable x with δ(x) = i, we have:…”

Section: Algorithmmentioning

confidence: 99%

Integrating Standard Dependency Schemes in QCSP Solvers

Jin

Zhang

2012

J. Comput. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Dependency schemes [30] based on [4,5], which are relations over variables, can be regarded as a generalization of tree-shaped quantifier structure. Given a dependency scheme D, a variable x is associated with all the variables y that "depend" on x with respect to D. Informally, if y depends on x, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Quantifier prefixes of PCNFs as well as quantifier trees fit into that framework since dependency schemes can be obtained from the prefix or the tree, respectively. Sophisticated dependency schemes were introduced in [30], all of which can be computed efficiently by syntactically analyzing PCNFs. .…”

Section: Introductionmentioning

confidence: 99%

“…This applies to reconstructed quantifier trees as well as considering treeshaped structure present in non-PCNFs. For example, the standard dependency scheme D std [30] is superior to tree-based approaches since it is deterministic and yields less dependencies. 1 This was pointed out in Ex.…”

Section: Introductionmentioning

confidence: 99%

“…This generalizes quantifier trees. Dependency DAGs can be obtained from dependency schemes such as the ones introduced in [30]. When integrating dependency DAGs in QBF solvers, the drawbacks of tree-shaped quantifier structure as pointed out above can be overcome.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Integrating Dependency Schemes in Search-Based QBF Solvers

Lonsing

Biere

2010

Theory and Applications of Satisfiability Testing – SAT 2010

View full text Add to dashboard Cite

Abstract. Many search-based QBF solvers implementing the DPLL algorithm for QBF (QDPLL) process formulae in prenex conjunctive normal form (PCNF). The quantifier prefix of PCNFs often results in strong variable dependencies which can influence solver performance negatively. A common approach to overcome this problem is to reconstruct quantifier structure e.g. by quantifier trees. Dependency schemes are a generalization of quantifier trees in the sense that more general dependency graphs can be obtained. So far, dependency graphs have not been applied in QBF solving. In this work we consider the problem of efficiently integrating dependency graphs in QDPLL. Thereby we generalize related work on integrating quantifier trees. By analyzing the core parts of QDPLL, we report on modifications necessary to profit from general dependency graphs. In comprehensive experiments we show that QDPLL using a particular dependency graph, despite of increased overhead, outperforms classical QDPLL relying on quantifier prefixes of PCNFs.

show abstract