Relational queries computable in polynomial time
Information and Control
Languages that capture complexity classes
SIAM Journal on Computing
A First-Order Isomorphism Theorem
SIAM Journal on Computing
Fixed-Point Logics on Planar Graphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
Finding reductions automatically
Fields of logic and computation
Abstraction-based algorithm for 2QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Solving hard ASP programs efficiently
LPNMR'05 Proceedings of the 8th international conference on Logic Programming and Nonmonotonic Reasoning
The seventh QBF solvers evaluation (QBFEVAL’10)
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Solving QBF with counterexample guided refinement
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
Fixed-point definability and polynomial time on graphs with excluded minors
Journal of the ACM (JACM)
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Reductions are perhaps the most useful tool in complexity theory and, naturally, it is in general undecidable to determine whether a reduction exists between two given decision problems. However, asking for a reduction on inputs of bounded size is essentially a $\Sigma^p_2$ problem and can in principle be solved by ASP, QBF, or by iterated calls to SAT solvers. We describe our experiences developing and benchmarking automatic reduction finders. We created a dedicated reduction finder that does counter-example guided abstraction refinement by iteratively calling either a SAT solver or BDD package. We benchmark its performance with different SAT solvers and report the tradeoffs between the SAT and BDD approaches. Further, we compare this reduction finder with the direct approach using a number of QBF and ASP solvers. We describe the tradeoffs between the QBF and ASP approaches and show which solvers perform best on our $\Sigma^p_2$ instances. It turns out that even state-of-the-art solvers leave a large room for improvement on problems of this kind. We thus provide our instances as a benchmark for future work on $\Sigma^p_2$ solvers.