The theory of combinatorial designs has always been a rich source of structured, parametrized families of SAT instances. On one hand, design theory provides interesting problems for testing various SAT solvers; on the other hand, high-performance SAT solvers provide an alternative tool for attacking open problems in design theory, simply by encoding problems as propositional formulas, and then searching for their models using off-the-shelf general purpose SAT solvers. This chapter presents several case studies of using SAT solvers to solve hard design theory problems, including quasigroup problems, Ramsey numbers, Van der Waerden numbers, covering arrays, Steiner systems, and Mendelsohn designs. It is shown that over a hundred of previously-open design theory problems were solved by SAT solvers, thus demonstrating the significant power of modern SAT solvers. Moreover, the chapter provides a list of 30 open design theory problems for the developers of SAT solvers to test their new ideas and weapons.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com