A new algorithm for deciding the satisfiability of polynomial formulas over the reals is proposed. The key point of the algorithm is a new projection operator, called sample-cell projection operator, custom-made for Conflict-Driven Clause Learning (CDCL)-style search. Although the new operator is also a CAD (Cylindrical Algebraic Decomposition)-like projection operator which computes the cell (not necessarily cylindrical) containing a given sample such that each polynomial from the problem is sign-invariant on the cell, it is of singly exponential time complexity. The sample-cell projection operator can efficiently guide CDCL-style search away from conflicting states. Experiments show the effectiveness of the new algorithm.

中文翻译：

---

用样本单元投影求解多项式公式的可满足性

提出了一种确定多项式公式在实数上的可满足性的新算法。该算法的关键点是一个新的投影算子，称为样本单元投影算子，为冲突驱动子句学习（CDCL）式搜索定制。虽然新的算子也是一个类似于 CAD（圆柱代数分解）的投影算子，它计算包含给定样本的单元（不一定是圆柱），这样问题中的每个多项式在单元上都是符号不变的，它是单指数的时间复杂度。样本单元投影算子可以有效地引导 CDCL 式搜索远离冲突状态。实验证明了新算法的有效性。