In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem $\Pi$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions -- we encode the problem of finding a plan for $\Pi$ with bound $n$ as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed-$\exists$ encodings. More importantly, we prove that for any given bound, it is never the case that the latter two encodings allow finding a valid plan while ours does not. On the experimental side, we consider 6 other planning systems -- including the ones which participated in this year's International Planning Competition (IPC) -- and we show that our planner Patty has remarkably good comparative performances on this year's IPC problems.

翻译：本文提出了一种求解线性数值规划问题的新方法，称为符号模式规划。给定规划问题$\Pi$、界值$n$以及一个模式（定义为任意动作序列），我们将寻找$\Pi$在界值$n$下可行规划的问题编码为一个公式，该公式的变量和/或子句数量少于当前最先进的滚动编码与松弛-松弛-$\exists$编码。更重要的是，我们证明对于任意给定界值，后两种编码能够找到有效规划的情况，我们的编码均不会失效。在实验方面，我们对比了其他6个规划系统（包括参与本年度国际规划竞赛IPC的系统），结果表明我们的规划器Patty在本年度IPC问题上展现出显著优越的比较性能。