Solving difficult SAT instances in the presence of symmetry

@inproceedings{Aloul2002SolvingDS,
  title={Solving difficult SAT instances in the presence of symmetry},
  author={F. Aloul and A. Ramani and I. Markov and K. Sakallah},
  booktitle={DAC '02},
  year={2002}
}
Research in algorithms for Boolean satisfiability and their implementations [23, 6] has recently outpaced benchmarking efforts. Most of the classic DIMACS benchmarks [10] can be solved in seconds on commodity PCs. More recent benchmarks take longer to solve because of their large size, but are still solved in minutes [25]. Yet, small and difficult SAT instances must exist because Boolean satisfiability is NP-complete.We propose an improved construction of symmetry-breaking clauses [9] and apply… Expand
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References

SHOWING 1-10 OF 50 REFERENCES
Faster SAT and smaller BDDs via common function structure
  • F. Aloul, I. Markov, K. Sakallah
  • Computer Science
  • IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281)
  • 2001
TLDR
This work points out that SAT and BDD techniques can be improved via the use of the same structural properties of instances, and proposes methods based on efficient problem partitioning that often outperforms existing techniques by a factor of two or more. Expand
The Efficiency of Resolution and Davis--Putnam Procedures
TLDR
This work gives an algorithm for unsatisfiability that when given an unsatisfiable formula of F finds a resolution proof of F, and investigates a class of backtrack search algorithms for producing resolution refutations of unsatisfiability, commonly known as Davis--Putnam procedures, and gives the first asymptotically tight average-case complexity analysis for their behavior on random formulas. Expand
Tractability through symmetries in propositional calculus
TLDR
This work proves for the first time the unsatisfiability of Ramsey's problem (17 vertices and three colors) which has been the subject of much research. Expand
Symmetry Reductions in Model Checking
TLDR
It is proved that the orbit problem is equivalent to an important problem in computational group theory which is at least as hard as the graph isomorphism but not known to be NP-complete. Expand
Finding hard instances of the satisfiability problem: A survey
TLDR
The performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions are considered. Expand
A comparative study of two Boolean formulations of FPGA detailed routing constraints
TLDR
It is demonstrated that the route-based formulation of Boolean SAT-based routing yields an easier-to-evaluate and more scalable routability Boolean function than the track-based method, providing empirical evidence that a smart/efficient Boolean formulation can achieve significant performance improvement in real-world applications. Expand
Symmetry-Breaking Predicates for Search Problems
TLDR
This work presents a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory, and discusses methods for generating partial symmetry-breaking predicates, and shows that in several speciic cases asymmetries can be broken either fully or partially using a polynomial number of predicates. Expand
Better verification through symmetry
TLDR
This work provides a proof of the soundness of the new symmetry-based verification algorithm based on a definition of the formal semantics of a simple description language with scalarsets, and leads to an alternative characterization of data independence. Expand
GRASP: A Search Algorithm for Propositional Satisfiability
TLDR
Experimental results obtained from a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for aLarge number of representative classes of SAT instances. Expand
GRASP-A new search algorithm for satisfiability
TLDR
Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for aLarge number of representative classes of SAT instances. Expand
...
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2
3
4
5
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