CAQE: A Certifying QBF Solver

Rabe, Markus N.; Tentrup, Leander

doi:10.1109/fmcad.2015.7542263

Cited by 80 publications

(94 citation statements)

References 20 publications

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“…All the state-of the-art QCSP solvers have the same drawback: they explore much larger combinatorial spaces than the natural search space of the original problem. In [3], the meaning of the "Achilles'heel" notion, initially introduced for Quantified Boolean Formulas (QBF) [8,23,28,29] in [2] as the difficulty to detect that the Boolean constraints are necessarily true under some partial assignment, has been extended for QCSP to the larger problem of how to avoid the exploration of combinatorial spaces that are known to be useless by construction. This definition includes the capture of the illegal actions of the player B but also for example the end of the game before the last turn that is also a source of oversized explored search space.…”

Section: Discussionmentioning

confidence: 99%

Quantified Constraint Handling Rules

Brault¹,

Stéphan²

2019

Electron. Proc. Theor. Comput. Sci.

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We shift the QCSP (Quantified Constraint Satisfaction Problems) framework to the QCHR (Quantified Constraint Handling Rules) framework by enabling dynamic binder and access to user-defined constraints. QCSP offers a natural framework to express PSPACE problems as finite two-players games. But to define a QCSP model, the binder must be formerly known and cannot be built dynamically even if the worst case won't occur. To overcome this issue, we define the new QCHR formalism that allows to build the binder dynamically during the solving. Our QCHR models exhibit state-of-the-art performances on static binder and outperforms previous QCSP approaches when the binder is dynamic.

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Section: Discussionmentioning

confidence: 99%

Quantified Constraint Handling Rules

Brault¹,

Stéphan²

2019

Electron. Proc. Theor. Comput. Sci.

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“…While variants of the problem have been studied since long [17], [3], there has been significant recent interest in designing practically efficient algorithms for Boolean functional synthesis. The resulting breed of algorithms [14], [23], [22], [11], [25], [18], [13], [2], [1], [15], [7], [24] have been empirically shown to work well on large collections of benchmarks. Nevertheless, there are not-so-large examples that are currently not solvable within reasonable resources by any known algorithm.…”

Section: Introductionmentioning

confidence: 99%

Knowledge Compilation for Boolean Functional Synthesis

Akshay

Arora

Chakraborty

et al. 2019

2019 Formal Methods in Computer Aided Design (FMCAD)

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Given a Boolean formula F (X, Y), where X is a vector of outputs and Y is a vector of inputs, the Boolean functional synthesis problem requires us to compute a Skolem function vector Ψ(Y) for X such that F (Ψ(Y), Y) holds whenever ∃X F (X, Y) holds. In this paper, we investigate the relation between the representation of the specification F (X, Y) and the complexity of synthesis. We introduce a new normal form for Boolean formulas, called SynNNF, that guarantees polynomialtime synthesis and also polynomial-time existential quantification for some order of quantification of variables. We show that several normal forms studied in the knowledge compilation literature are subsumed by SynNNF, although SynNNF can be super-polynomially more succinct than them. Motivated by these results, we propose an algorithm to convert a specification in CNF to SynNNF, with the intent of solving the Boolean functional synthesis problem. Experiments with a prototype implementation show that this approach solves several benchmarks beyond the reach of state-of-the-art tools.• We present a new sub-class of negation normal form, called SynNNF, that admits polynomial-time synthesis and quantifier elimination for a set of variables.

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“…2QBF solvers based on CEGAR/CEGIS search for universal assignments and matching existential assignments using two SAT solvers [5,20,21]. There are several generalizations of this approach to QBF with more than one quantifier alternation [22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Understanding and Extending Incremental Determinization for 2QBF

Rabe

Tentrup

Rasmussen

et al. 2018

Computer Aided Verification

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Incremental determinization is a recently proposed algorithm for solving quantified Boolean formulas with one quantifier alternation. In this paper, we formalize incremental determinization as a set of inference rules to help understand the design space of similar algorithms. We then present additional inference rules that extend incremental determinization in two ways. The first extension integrates the popular CEGAR principle and the second extension allows us to analyze different cases in isolation. The experimental evaluation demonstrates that the extensions significantly improve the performance.

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CAQE: A Certifying QBF Solver

Cited by 80 publications

References 20 publications

Quantified Constraint Handling Rules

Quantified Constraint Handling Rules

Knowledge Compilation for Boolean Functional Synthesis

Understanding and Extending Incremental Determinization for 2QBF

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