A More Efficient BDD-Based QBF Solver

Olivo, Oswaldo

doi:10.1007/978-3-642-23786-7_51

Cited by 9 publications

(22 citation statements)

References 18 publications

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“…We use this preprocessor in our experiments. Our work reduces the upper complexity bounds for unit and pure literal rules for BDDs presented in [16] . The algorithms for Universal Reduction, Forced Literals and Trivial Falsity that we propose have common ideas with clause Learning for QBFs [12] , since our methods can be considered as a form of internal clause learning within BDDs, rather than learning from the entire formula.…”

Section: Related Workmentioning

confidence: 97%

“…[16] Let f be a non-trivial propositional formula over variables x 1 , ...., x n . Then l is a BDD unit clause in BDD(f ) iff (Restrict(BDD(f ), BDD(¬l)) = 0).…”

Section: Bdd Constraint Propagationmentioning

confidence: 99%

“…We now describe unit clause and pure literal propagation over BDDs, based on the generalizations of their CNF counterparts; these rules constitute the BDD constraint propagation routine initially described in [16].…”

Section: Bdd Constraint Propagationmentioning

confidence: 99%

“…It has been argued that this fact is largely due to the elaborate optimizations implemented in the DPLL framework over the years , especially unit propagation for SAT and universal reduction for QBF, as well as ingenious variable selection heuristics. In spite of this, recent efforts have shown that resolution algorithms can outperform guessing in the verification benchmarks [18] [16]. A recent approach involves the use of Binary Decision Diagrams(BDDs) and a simplification routine called BDD constraint propagation [16] .…”

Section: Introductionmentioning

confidence: 99%

“…In spite of this, recent efforts have shown that resolution algorithms can outperform guessing in the verification benchmarks [18] [16]. A recent approach involves the use of Binary Decision Diagrams(BDDs) and a simplification routine called BDD constraint propagation [16] . The main idea consisted in adapting optimizations from search-based solvers within the context of BDDs.…”

Section: Introductionmentioning

confidence: 99%

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Improved Binary Decision Diagram Constraint Propagation for Satisfiability Problems

Olivo

2012

2012 31st International Conference of the Chilean Computer Science Society

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In general, search-based solvers have been dominating symbolic solvers according to experimental results reported in the SAT and QBF literature. However, some recent efforts have contributed to close that performance gap. One novel approach involves the use of Binary Decision Diagrams(BDDs) and a simplification routine called BDD constraint propagation. The main idea is to adapt optimizations from search-based solvers in the context of BDDs. In this paper we improve upon the existing BDD constraint propagation procedure. Concretely, for a BDD A and its support set SupportSet(A), we reduce the asymptotic upper bound for the clause BDD pure literal extraction from O(A * SupportSet(A)) to O(n) time and nonclause BDD unit literal extraction from O(A * SupportSet(A)) to O(A) time. We also formulate for the first time the Trivial Falsity, Forced Literal and Universal Reduction rules for BDDs. We show in the experimental section that these improvements allow a BDD-based solver to tackle new families of problems, and outperform state-of-the art solvers in some cases.

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Section: Related Workmentioning

confidence: 97%

“…[16] Let f be a non-trivial propositional formula over variables x 1 , ...., x n . Then l is a BDD unit clause in BDD(f ) iff (Restrict(BDD(f ), BDD(¬l)) = 0).…”

Section: Bdd Constraint Propagationmentioning

confidence: 99%

Section: Bdd Constraint Propagationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Binary Decision Diagram Constraint Propagation for Satisfiability Problems

Olivo

2012

2012 31st International Conference of the Chilean Computer Science Society

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Non-clausal Redundancy Properties

Barnett

Biere

2021

Automated Deduction – CADE 28

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State-of-the-art refutation systems for SAT are largely based on the derivation of clauses meeting some redundancy criteria, ensuring their addition to a formula does not alter its satisfiability. However, there are strong propositional reasoning techniques whose inferences are not easily expressed in such systems. This paper extends the redundancy framework beyond clauses to characterize redundancy for Boolean constraints in general. We show this characterization can be instantiated to develop efficiently checkable refutation systems using redundancy properties for Binary Decision Diagrams (BDDs). Using a form of reverse unit propagation over conjunctions of BDDs, these systems capture, for instance, Gaussian elimination reasoning over XOR constraints encoded in a formula, without the need for clausal translations or extension variables. Notably, these systems generalize those based on the strong Propagation Redundancy (PR) property, without an increase in complexity.

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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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A More Efficient BDD-Based QBF Solver

Cited by 9 publications

References 18 publications

Improved Binary Decision Diagram Constraint Propagation for Satisfiability Problems

Improved Binary Decision Diagram Constraint Propagation for Satisfiability Problems

Non-clausal Redundancy Properties

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

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