Fixed-Parameter Tractable Reductions to SAT

Today’s SAT solvers have an enormous importance and impact in many practical settings. They are used as efficient back-end to solve many NP-complete problems. However, many computational problems are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. In certain cases one can break through these complexity barriers by fixed-parameter tractable (fpt) reductions which exploit structural aspects of problem instances in terms of problem parameters. Recent research established a general theoretical framework that supports the classification of parameterized problems on whether they admit such an fpt-reduction to SAT or not. We use this framework to analyze some problems that are related to Boolean satisfiability. We consider several natural parameterizations of these problems, and we identify for which of these an fpt-reduction to SAT is possible. The problems that we look at are related to minimizing an implicant of a DNF formula, minimizing a DNF formula, and satisfiability of quantified Boolean formulas. 1 Institute of Information Systems, Vienna University of Technology, Vienna, Austria ∗ Supported by the European Research Council (ERC), project 239962 (COMPLEX REASON), and the Austrian Science Fund (FWF), project P26200 (Parameterized Compilation). Publication Information: This is the authors’ self-archived copy of a paper that appeared in the Proceedings of the 17th International Symposium on the Theory and Applications of Satisfiability Testing (SAT 2014), dx.doi.org/10.1007/978-3-319-09284-3 8. The final publication is available at www.springer.com. 2 INFSYS RR 1843-14-04