We show how to aggressively add uninferred constraints, in a controlled manner, to formulae for finding Van der Waerden numbers during search. We show that doing so can improve the performance of standard SAT solvers on these formulae by orders of magnitude. We obtain a new and much greater lower bound for one of the Van der Waerden numbers, specifically a bound of 1132 for W(2,6). We believe this bound to actually be the number we seek. The structure of propositional formulae for solving Van der Waerden numbers is similar to that of formulae arising from Bounded Model Checking. Therefore, we view this as a preliminary investigation into solving hard formulae in the area of Formal Verification.
展开▼
机译：我们展示了如何以受控方式积极地添加无穷详细的约束，以在搜索期间查找范德·沃尔顿号码的公式。我们表明，这样做可以通过数量级来提高标准SAT求解器对这些公式的性能。我们为van der Waerden号码中的一个新的和更大的下限，特别是为W（2,6）的1132的界限。我们相信这一定实际上是我们寻求的数字。用于求解van der Waerden号码的命题公式的结构类似于有界模型检查产生的公式的结构。因此，我们认为这是在正式验证领域解决硬质合理的初步调查。
展开▼
