Evaluating and certifying QBFs: A comparison of state-of-the-art tools

Narizzano, Massimo; Peschiera, Claudia; Pulina, Luca; Tacchella, Armando

doi:10.3233/aic-2009-0468

Cited by 18 publications

(9 citation statements)

References 31 publications

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“…A number of works focus on the certification of QBF solvers (e.g. [6,35,39,26]) motivated by error prevention [10], but also because the certificates themselves can be useful (e.g. [25,49,45,4,33]).…”

Section: Related Workmentioning

confidence: 99%

On QBF Proofs and Preprocessing

Janota

Grigore

Marques-Silva

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e.g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.

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Section: Related Workmentioning

confidence: 99%

On QBF Proofs and Preprocessing

Janota

Grigore

Marques-Silva

2013

Logic for Programming, Artificial Intelligence, and Reasoning

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“…Currently, there is little standardization of the proof capabilities or the proof systems supported by different QBF solvers [21]. Some solvers can generate syntactic certificates-ones that can be directly checked by a proof checker.…”

Section: Introductionmentioning

confidence: 99%

“…An even larger number of solvers can generate semantic certificates in the form of Herbrand functions for false formulas and Skolem functions for true ones, describing how to instantiate either the universal or the existential variables [21]. These can be used to expand the original formula into a (often much larger) Boolean formula that is checked with a SAT solver [22] or with a high-degree polynomial algorithm [25].…”

Section: Introductionmentioning

confidence: 99%

Dual Proof Generation for Quantified Boolean Formulas with a BDD-based Solver

Bryant

Heule

2021

Automated Deduction – CADE 28

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Existing proof-generating quantified Boolean formula (QBF) solvers must construct a different type of proof depending on whether the formula is false (refutation) or true (satisfaction). We show that a QBF solver based on ordered binary decision diagrams (BDDs) can emit a single dual proof as it operates, supporting either outcome. This form consists of a sequence of equivalence-preserving clause addition and deletion steps in an extended resolution framework. For a false formula, the proof terminates with the empty clause, indicating conflict. For a true one, it terminates with all clauses deleted, indicating tautology. Both the length of the proof and the time required to check it are proportional to the total number of BDD operations performed. We evaluate our solver using a scalable benchmark based on a two-player tiling game.

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“…Modern QBF solvers not only decide the satisfiability of a formula, but also produce certificates [5][6][7][8][9][10][11][12][13][14]. Such a certificate is either syntactical or semantical.…”

Section: Introductionmentioning

confidence: 99%

Skolem Function Continuation for Quantified Boolean Formulas

et al. 2017

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Modern solvers for quantified Boolean formulas (QBF) not only decide the satisfiability of a formula, but also return a set of Skolem functions representing a model for a true QBF. Unfortunately, in combination with a preprocessor this ability is lost for many preprocessing techniques. A preprocessor rewrites the input formula to an equi-satisfiable formula which is often easier to solve than the original formula. Then the Skolem functions returned by the solver represent a solution for the preprocessed formula, but not necessarily for the original encoding. Our solution to this problem is to combine Skolem functions obtained from a QRAT trace as produced by the widely-used preprocessor Bloqqer with Skolem functions for the preprocessed formula. This approach is agnostic of the concrete rewritings performed by the preprocessor and allows the combination of Bloqqer with any Skolem function producing solver, hence realizing a smooth integration into the solving tool chain.

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Evaluating and certifying QBFs: A comparison of state-of-the-art tools

Cited by 18 publications

References 31 publications

On QBF Proofs and Preprocessing

On QBF Proofs and Preprocessing

Dual Proof Generation for Quantified Boolean Formulas with a BDD-based Solver

Skolem Function Continuation for Quantified Boolean Formulas

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