Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Many hard examples for resolution
Journal of the ACM (JACM)
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Symbolic model checking: 1020 states and beyond
Information and Computation - Special issue: Selections from 1990 IEEE symposium on logic in computer science
The hardest constraint problems: a double phase transition
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
Generating hard satisfiability problems
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
On the complexity of unsatisfiability proofs for random k-CNF formulas
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
Symbolic model checking using SAT procedures instead of BDDs
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A machine program for theorem-proving
Communications of the ACM
Early Quantification and Partitioned Transition Relations
ICCD '96 Proceedings of the 1996 International Conference on Computer Design, VLSI in Computers and Processors
Random 3-SAT: The Plot Thickens
CP '02 Proceedings of the 6th 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
VIS: A System for Verification and Synthesis
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
ZRES: The Old Davis-Putman Procedure Meets ZBDD
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Equivalence checking using abstract BDDs
ICCD '97 Proceedings of the 1997 International Conference on Computer Design (ICCD '97)
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Comparing phase transitions and peak cost in PP-complete satisfiability problems
Eighteenth national conference on Artificial intelligence
On the typical case complexity of graph optimization
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Symbolic Techniques in Satisfiability Solving
Journal of Automated Reasoning
Inferring non-suspension conditions for logic programs with dynamic scheduling
ACM Transactions on Computational Logic (TOCL)
Implementing semantic merging operators using binary decision diagrams
International Journal of Approximate Reasoning
On the typical case complexity of graph optimization
Discrete Applied Mathematics
Horn upper bounds and renaming
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Applying UCT to boolean satisfiability
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Monte-carlo style UCT search for boolean satisfiability
AI*IA'11 Proceedings of the 12th international conference on Artificial intelligence around man and beyond
Experimental evaluation of classical automata constructions
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Search vs. symbolic techniques in satisfiability solving
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Resolution tunnels for improved SAT solver performance
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
| Hi-index | 0.00 |
This paper contains an experimental study of the impact of the construction strategy of reduced, ordered binary decision diagrams (ROBDDs) on the average-case computational complexity of random 3-SAT, using the CUDD package. We study the variation of median running times for a large collection of random 3-SAT problems as a function of the density as well as the order (number of variables) of the instances. We used ROBDD-based pure SAT-solving algorithms, which we obtained by an aggressive application of existential quantification, augmented by several heuristic optimizations. Our main finding is that our algorithms display an "easy-hard-less-hard" pattern that is quite similar to that observed earlier for search-based solvers. When we start with low-density instances and then increase the density, we go from a region of polynomial running time, to a region of exponential running time, where the exponent first increases and then decreases as a function of the density. The locations of both transitions, from polynomial to exponential and from increasing to decreasing exponent, are algorithm dependent. In particular, the running time peak is quite independent from the crossover density of 4.26 (where the probability of satisfiability declines precipitously); it occurs at density 3.8 for one algorithm and at density 2.3 for for another, demonstrating that the correlation between the crossover density and computational hardness is algorithm dependent.