Resolution for Quantified Boolean Formulas

Büning, Hans Kleine; Karpiński, Marek; Flögel, Andreas

doi:10.1006/inco.1995.1025

Cited by 261 publications

(207 citation statements)

References 5 publications

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“…Moreover, (inc)DepQBF and other search-based QBF solvers rely on Q-resolution [19] as the underlying proof system. Given a Q-resolution proof Π of the unsatisfiability of a QBF ψ, it is possible to extract from Π a countermodel [2] or strategy [15] of ψ in terms of a set of Herbrand functions.…”

Section: Comparison To Heuristic Approachesmentioning

confidence: 99%

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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Section: Comparison To Heuristic Approachesmentioning

confidence: 99%

Conformant Planning as a Case Study of Incremental QBF Solving

Egly

Kronegger

Lonsing

et al. 2014

Artificial Intelligence and Symbolic Computation

View full text Add to dashboard Cite

show abstract

“…Given a QBF ψ = P.φ and a clause C ∈ φ, universal reduction [7] produces the clause C := reduce(C) := C \{l | quant(l) = ∀ and ∀e ∈ C : quant(e) = ∃ → lev(e) < lev(l)} by removing all universal literals from C which have a maximal quantification level. Universal reduction on ψ produces the QBF resulting from ψ by the application of universal reduction to each clause in φ.…”

Section: Preliminariesmentioning

confidence: 99%

“…Q-resolution [7] is a restriction of resolution. Given two non-tautological clauses C l and C r and an existential pivot variable p, the Q-resolvent is defined as follows.…”

Section: Preliminariesmentioning

confidence: 99%

“…A common approach is search-based QBF solving with conflict-driven clause learning (CDCL) [2,11], which is related to propositional logic (SAT solving) in that it extends the DPLL algorithm [3]. In addition to solving the QBF decision problem, QBF solvers with clause learning are able to produce Q-resolution proofs [7] to certify their answer. These proofs can be used to obtain solutions to problems encoded as QBFs.…”

Section: Introductionmentioning

confidence: 99%

“…First, we show that formulas of a certain family of QBFs [7] have LDQ-resolution proofs of polynomial size in the length of the formula. According to [7], any Q-resolution proof of these formulas is exponential.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving

Egly

Lonsing

Widl

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. Strategies (and certificates) for quantified Boolean formulas (QBFs) are of high practical relevance as they facilitate the verification of results returned by QBF solvers and the generation of solutions to problems formulated as QBFs. State of the art approaches to obtain strategies require traversing a Q-resolution proof of a QBF, which for many real-life instances is too large to handle. In this work, we consider the long-distance Q-resolution (LDQ) calculus, which allows particular tautological resolvents. We show that for a family of QBFs using the LDQ-resolution allows for exponentially shorter proofs compared to Q-resolution. We further show that an approach to strategy extraction originally presented for Q-resolution proofs can also be applied to LDQ-resolution proofs. As a practical application, we consider search-based QBF solvers which are able to learn tautological clauses based on resolution and the conflict-driven clause learning method. We prove that the resolution proofs produced by these solvers correspond to proofs in the LDQ calculus and can therefore be used as input for strategy extraction algorithms. Experimental results illustrate the potential of the LDQ calculus in search-based QBF solving.

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On deciding the non‐emptiness of 2SAT polytopes with respect to First Order Queries

Subramani

2004

Mathematical Logic Qtrly

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Key words 2SAT polytope, first order query, lattice point problem, quantified lattice point problem, NPcomplete, PSPACE-complete. MSC (2000) 03D15, 68Q15, 68Q20This paper is concerned with techniques for identifying simple and quantified lattice points in 2SAT polytopes. 2SAT polytopes generalize the polyhedra corresponding to Boolean 2SAT formulas, Vertex-Packing (Covering, Partitioning) and Network flow problems; they find wide application in the domains of Program verification (Software Engineering) and State-Space search (Artificial Intelligence). Our techniques are based on the symbolic elimination strategy called the Fourier-Motzkin elimination procedure and thus have the advantages of being extremely simple (from an implementational perspective) and incremental. We also provide a characterization of a 2SAT polytope in terms of its extreme points and derive some interesting hardness results for associated optimization problems. Finally, we provide a brief discussion on the maximum size of a subdeterminant of the linear system representing a 2SAT polytope; this parameter plays a vital role in deriving analytical bounds on the size of the search space for checking whether the polyhedron includes a lattice point.

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Resolution for Quantified Boolean Formulas

Cited by 261 publications

References 5 publications

Conformant Planning as a Case Study of Incremental QBF Solving

Conformant Planning as a Case Study of Incremental QBF Solving

Long-Distance Resolution: Proof Generation and Strategy Extraction in Search-Based QBF Solving

On deciding the non‐emptiness of 2SAT polytopes with respect to First Order Queries

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