Charles Jordan

Experiments with reduction finding

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

MPIDepQBF: Towards Parallel QBF Solving without Knowledge Sharing

\Sigma^p_2

mplrs : A scalable parallel vertex/facet enumeration code

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

Relational properties expressible with one universal quantifier are testable

\Sigma^p_2

Untestable properties in the kahr-moore-wang class

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

A note on the testability of ramsey's class

\Sigma^p_2

Untestable properties expressible with four first-order quantifiers

solvers.

Experimental descriptive complexity

Inspired by recent work on parallel SAT solving, we present a lightweight approach for solving quantified Boolean formulas (QBFs) in parallel. In particular, our approach uses a sequential state-of-the-art QBF solver to evaluate subformulas in working processes. It abstains from globally exchanging information between the workers, but keeps learnt information only locally. To this end, we equipped the state-of-the-art QBF solver DepQBF with assumption-based reasoning and integrated it in our novel solver MPIDepQBF as backend solver. Extensive experiments on standard computers as well as on the supercomputer Tsubame show the impact of our approach.

The QBFGallery 2014: The QBF Competition at the FLoC Olympic Games

We describe a new parallel implementation, mplrs, of the vertex enumeration code lrs that uses the MPI parallel environment and can be run on a network of computers. The implementation makes use of a C wrapper that essentially uses the existing lrs code with only minor modifications. mplrs was derived from the earlier parallel implementation plrs, written by G. Roumanis in C