SAT and Interactions

Summary

Brief Introduction to the Topic

Propositional satisfiability (or Boolean satisfiability) is the problem of determining whether the variables of a Boolean formula can be assigned truth values in such a way as to make the formula true. This satisfiability problem, SAT for short, stands at the crossroads of logic, graph theory, computer science, computer engineering and computational physics. Indeed, many problems originating from one of these fields typically have multiple translations to satisfiability. Unsurprisingly, SAT is of central importance in various areas of computer science including algorithmics, verification, planning, hardware design and artificial intelligence. It can express a wide range of combinatorial problems as well as many real-world ones.

SAT is very significant from a theoretical point of view. Since the Cook-Levin theorem, which identified SAT as the first NP-complete problem, it has become a reference for an enormous variety of complexity statements. The most prominent one is the question "is P equal to NP?" Proving that SAT is not in P would answer this question negatively. Restrictions and generalizations of the propositional satisfiability problem play a similar rôle in the examination of other complexity classes and relations among them. In particular, quantified versions of SAT (QSAT, in which Boolean variables are universally or existentially quantified) as well as variants of SAT in which some notion of minimality is involved, provide prototypical complete problems for every level of the polynomial hierarchy.

During the past three decades, an impressive array of diverse techniques from mathematical fields, such as propositional and first-order logic, model theory, Boolean function theory, complexity, combinatorics and probability, has contributed to a better understanding of the SAT problem. Although significant progress has been made on several fronts, most of the central questions remain unsolved so far.

One of the main aims of the Dagstuhl seminar was to bring together researchers from different areas of activity in SAT so that they can communicate state-of-the-art advances and embark on a systematic interaction that will enhance the synergy between the different areas.

Concluding Remarks and Future Plans

The organizers regard the seminar as a great success. Bringing together researchers from different areas of theoretical computer science fostered valuable interactions and led to fruitful discussions. Feedback from the participants was very positive as well. Many attendants expressed their wish for a continuation.

Finally, the organizers wish to express their gratitude toward the Scientific Directorate of the Center for its support of this seminar, and hope to be able to continue this series of seminars on SAT and Interactions in the future.