A First Step Towards a Unified Proof Checker for QBF

Jussila, Toni; Biere, Armin; Sinz, Carsten; Kröning, Daniel; Wintersteiger, Christoph M.

doi:10.1007/978-3-540-72788-0_21

Cited by 39 publications

(50 citation statements)

References 24 publications

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“…Additionally, unit clauses learnt by PicoSAT are propagated using QBF-specific QBCP rules within QxBF. Table 1 compares the impact of different FL approaches on the performance of QBF solvers based on search (DepQBF [17] and QuBE7.1 [10]) and variable elimination (Quantor [2], squolem [15] and Nenofex [16]) using all benchmarks from QBFEVAL'10 [20]. For QuBE7.1 internal preprocessing was disabled (QuBE7.1-np).…”

Section: Methodsmentioning

confidence: 99%

Failed Literal Detection for QBF

Lonsing

Biere

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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Abstract. Failed literal detection (FL) in SAT is a powerful approach for preprocessing. The basic idea is to assign a variable as assumption. If boolean constraint propagation (BCP) yields an empty clause then the negated assumption is necessary for satisfiability. Whereas FL is common in SAT, it cannot easily be applied to QBF due to universal quantification. We present two approaches for FL to preprocess prenex CNFs. The first one is based on abstraction where certain universal variables are treated as existentially quantified. Second we combine QBF-specific BCP (QBCP) in FL with Q-resolution to validate assignments learnt by FL. Finally we compare these two approaches to a third common approach based on SAT. It turns out that the three approaches are incomparable. Experimental evaluation demonstrates that FL for QBF can improve the performance of search-and elimination-based QBF solvers.

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Section: Methodsmentioning

confidence: 99%

Failed Literal Detection for QBF

Lonsing

Biere

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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“…Thus, a QBF solver that returns an assignment for the top-level existential variables can compute suitable coefficients. Examples of such solvers are Quantor [9], sKizzo [10], and Squolem [11]. In our experiments, we use an experimental version of QuBE [12].…”

Section: Synthesis Of Ranking Functions From Templatesmentioning

confidence: 99%

“…3.2, we developed the prototype Seneschal. 11 It is based on the prover Princess [18] for Presburger arithmetic with uninterpreted predicates and works by (i) translating a given bit-vector program into a PA formula, (ii) eliminating the quantifiers in the formula, (iii) flattening the formula to a disjunction of systems of inequalities, and (iv) applying Lem. 3 to compute ranking functions.…”

Section: Experiments On Smaller Examplesmentioning

confidence: 99%

Ranking Function Synthesis for Bit-Vector Relations

Cook

Kroening

Rümmer

et al. 2010

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machine-level integers (bit-vectors) is an open problem. This is particularly relevant for the verification of low-level code. We propose several novel algorithms to generate ranking functions for relations over machine integers: a complete method based on a reduction to Presburger arithmetic, and a template-matching approach for predefined classes of ranking functions based on reduction to SAT-and QBF-solving. The utility of our algorithms is demonstrated on examples drawn from Windows device drivers.

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“…Effectively checking the result returned by a QBF solver has been an open challenge for a long time [1,2,3,4,5,6,7]. The current state-of-the-art is to simply dump Q-resolution proofs and to validate their structure.…”

Section: Introductionmentioning

confidence: 99%

A Unified Proof System for QBF Preprocessing

Heule

Seidl²,

Biere³

2014

Automated Reasoning

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Abstract. For quantified Boolean formulas (QBFs), preprocessing is essential to solve many real-world formulas. The application of a preprocessor, however, prevented the extraction of proofs for the original formula. Such proofs are required to independently validate correctness of the preprocessor's rewritings and the solver's result. Especially for universal expansion proof checking was not possible so far. In this paper, we introduce a unified proof system based on three simple and elegant quantified resolution asymmetric tautology (QRAT) rules. In combination with an extended version of universal reduction, they are sufficient to efficiently express all preprocessing techniques used in state-of-the-art preprocessors including universal expansion. Moreover, these rules give rise to new preprocessing techniques. We equip our preprocessor bloqqer with QRAT proof logging and provide a proof checker for QRAT proofs.

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A First Step Towards a Unified Proof Checker for QBF

Cited by 39 publications

References 24 publications

Failed Literal Detection for QBF

Failed Literal Detection for QBF

Ranking Function Synthesis for Bit-Vector Relations

A Unified Proof System for QBF Preprocessing

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