Bounded Universal Expansion for Preprocessing QBF

Bubeck, Uwe; Büning, Hans Kleine

doi:10.1007/978-3-540-72788-0_24

Cited by 39 publications

(49 citation statements)

References 8 publications

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“…They considered universal expansion (the "expand" operation in Quantor, which eliminates a universal variable). They showed in their Theorem 1 [4] and Theorem 5.6.1 [5] that the operation can be simplified by not expanding existential variables that meet a certain criterion called a one-sided dependency.…”

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confidence: 99%

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Gelder

2012

Lecture Notes in Computer Science

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Abstract. Recent solvers for quantified boolean formulas (QBFs) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. The underlying proof system is Q-resolution. This paper shows an exponential worst case for the clause-learning procedure. This finding confirms empirical observations that some formulas take mysteriously long times to solve, compared to other apparently similar formulas. Q-resolution is known to be refutation complete for QBF, but not all logically implied clauses can be derived with it. A stronger proof system called QU-resolution is introduced, and shown to be complete in this stronger sense. A new procedure called QPUP for clause learning without tautologies is also described. A generalization of pure literals is introduced, called effectively depthmonotonic literals. In general, the variable-elimination resolution operation, as used by Quantor, sQueezeBF, and Bloqqer is unsound if the existential variable being eliminated is not at innermost scope. It is shown that variable-elimination resolution is sound for effectively depthmonotonic literals even when they are not at innermost scope.

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confidence: 99%

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Gelder

2012

Lecture Notes in Computer Science

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“…Variable dependencies have been studied in a slightly different context by Ayari and Basin [3], Biere [5], and Bubeck and Kleine Büning [6]; of related interest is the work of Egly, Tompits, and Woltran on quantifier shiftings [11] and Benedetti's work on quantifier trees [4]. For a variable dependency scheme one needs to compromise between tractability and generality: we show in Section 3 that identifying minimal variable dependencies is PSpace-hard.…”

Section: Variable Dependenciesmentioning

confidence: 99%

“…For a variable dependency scheme one needs to compromise between tractability and generality: we show in Section 3 that identifying minimal variable dependencies is PSpace-hard. We propose two tractable dependency schemes that are reasonably general: the standard dependency scheme which is based on ideas of Ayari and Basin [3], Biere [5], and Bubeck and Kleine Büning [6], and the triangle dependency scheme which generalizes the standard dependency scheme without increasing the asymptotic worst-case runtime.…”

Section: Variable Dependenciesmentioning

confidence: 99%

“…The application of our dependency schemes is not limited to backdoor set optimization; we think that it is also useful for other aspects of the evaluation of quantified Boolean formulas. In the works of Ayari and Basin [3], Biere [5], and Bubeck and Kleine Büning [6], variable dependencies are used to identify clauses that have to be duplicated when eliminating universal variables by expansion. In particular, those clauses that contain variables that depend on the expanded variable (more precisely, variables for which it is unknown whether they are independent) have to be duplicated.…”

Section: Variable Dependenciesmentioning

confidence: 99%

“…Following the approaches of [3,5,6], as formalized in the standard dependency scheme, one has to duplicate the whole matrix when expanding x, since the standard dependency scheme is not able to identify any of the variables y 1 , . .…”

Section: Variable Dependenciesmentioning

confidence: 99%

See 2 more Smart Citations

Backdoor Sets of Quantified Boolean Formulas

Samer

Szeider

2008

J Autom Reasoning

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We generalize the notion of backdoor sets from propositional formulas to quantified Boolean formulas (QBF). This allows us to obtain hierarchies of tractable classes of quantified Boolean formulas with the classes of quantified Horn and quantified 2CNF formulas, respectively, at their first level, thus gradually generalizing these two important tractable classes. In contrast to known tractable classes based on bounded treewidth, the number of quantifier alternations of our classes is unbounded. As a side product of our considerations we develop a theory of variable dependency which is of independent interest.

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Conformant Planning as a Case Study of Incremental QBF Solving

Egly

Kronegger

Lonsing

et al. 2014

Artificial Intelligence and Symbolic Computation

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Abstract. We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on experiments with a workflow to incrementally encode a planning instance into a sequence of QBFs. To solve this sequence of successively constructed QBFs, we use our general-purpose incremental QBF solver DepQBF. Since the generated QBFs have many clauses and variables in common, our approach avoids redundancy both in the encoding phase and in the solving phase. Experimental results show that incremental QBF solving outperforms non-incremental QBF solving. Our results are the first empirical study of incremental QBF solving in the context of planning and motivate its use in other application domains.

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Bounded Universal Expansion for Preprocessing QBF

Cited by 39 publications

References 8 publications

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Backdoor Sets of Quantified Boolean Formulas

Conformant Planning as a Case Study of Incremental QBF Solving

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