Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
Formally verifying a microprocessor using a simulation methodology
DAC '94 Proceedings of the 31st annual Design Automation Conference
Experimental results on the application of satisfiability algorithms to scheduling problems
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Efficient and constructive algorithms for the pathwidth and treewidth of graphs
Journal of Algorithms
Binary decision diagrams and applications for VLSI CAD
Binary decision diagrams and applications for VLSI CAD
Symbolic model checking using SAT procedures instead of BDDs
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Model checking
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Partition-based decision heuristics for image computation using SAT and BDDs
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Early Quantification and Partitioned Transition Relations
ICCD '96 Proceedings of the 1996 International Conference on Computer Design, VLSI in Computers and Processors
A Compressed Breadth-First Search for Satisfiability
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Random 3-SAT and BDDs: The Plot Thickens Further
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Ordered Binary Decision Diagrams and the Davis-Putnam Procedure
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Efficient Model Checking by Automated Ordering of Transition Relation Partitions
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
FORCE: a fast and easy-to-implement variable-ordering heuristic
Proceedings of the 13th ACM Great Lakes symposium on VLSI
Checking satisfiability of a conjunction of BDDs
Proceedings of the 40th annual Design Automation Conference
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
BerkMin: A Fast and Robust Sat-Solver
Proceedings of the conference on Design, automation and test in Europe
Multi-resolution on compressed sets of clauses
ICTAI '00 Proceedings of the 12th IEEE International Conference on Tools with Artificial Intelligence
Random 3-SAT: The Plot Thickens
Constraints
Conformant planning via symbolic model checking
Journal of Artificial Intelligence Research
A structure-based variable ordering heuristic for SAT
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A direct construction of polynomial-size OBDD proof of pigeon hole problem
Information Processing Letters
Symbolic Techniques in Propositional Satisfiability Solving
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Solving difficult SAT problems by using OBDDs and greedy clique decomposition
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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Recent work has shown how to use binary decision diagrams for satisfiability solving. The idea of this approach, which we call symbolic quantifier elimination, is to view an instance of propositional satisfiability as an existentially quantified proposition formula. Satisfiability solving then amounts to quantifier elimination; once all quantifiers have been eliminated, we are left with either 1 or 0. Our goal in this work is to study the effectiveness of symbolic quantifier elimination as an approach to satisfiability solving. To that end, we conduct a direct comparison with the DPLL-based ZChaff, as well as evaluate a variety of optimization techniques for the symbolic approach. In comparing the symbolic approach to ZChaff, we evaluate scalability across a variety of classes of formulas. We find that no approach dominates across all classes. While ZChaff dominates for many classes of formulas, the symbolic approach is superior for other classes of formulas. Once we have demonstrated the viability of the symbolic approach, we focus on optimization techniques for this approach. We study techniques from constraint satisfaction for finding a good plan for performing the symbolic operations of conjunction and of existential quantification. We also study various variable-ordering heuristics, finding that while no heuristic seems to dominate across all classes of formulas, the maximum-cardinality search heuristic seems to offer the best overall performance.