Many planning formalisms allow for mixing numeric with Boolean effects. However, most of these formalisms are undecidable. In this paper, we will analyze possible causes for this undecidability by studying the number of different occurrences of actions, an approach that proved useful for metric fluents before. We will start by reformulating a numeric planning problem known as restricted tasks as a search problem. We will then show how an NP-complete fragment of numeric planning can be found by using heuristics. To achieve this, we will develop the idea of multi-valued partial order plans, a least committing compact representation for (sequential and parallel) plans. Finally, we will study optimization techniques for this representation to incorporate soft preconditions.

翻译：许多规划形式允许混合数字与布尔效应。然而，这些形式大多是不可判定的。本文将通过研究动作出现的不同次数来分析这种不可判定性的可能原因，该方法此前已被证明对度量流形有效。我们首先将一种称为受限任务的数字规划问题重新表述为搜索问题。随后展示如何通过启发式方法找到数字规划的一个NP完全片段。为此，我们将提出多值偏序规划的概念——一种适用于（串行与并行）规划的最小承诺紧凑表示。最后，我们将研究针对该表示形式的优化技术，以纳入软前提条件。