Recent research has examined algorithms to minimize robots' resource footprints. The class of combinatorial filters (discrete variants of widely-used probabilistic estimators) has been studied and methods for reducing their space requirements introduced. This paper extends existing combinatorial filters by introducing a natural generalization that we dub cover combinatorial filters. In addressing the new -- but still NP-complete -- problem of minimization of cover filters, this paper shows that multiple concepts previously believed to be true about combinatorial filters (and actually conjectured, claimed, or assumed to be) are in fact false. For instance, minimization does not induce an equivalence relation. We give an exact algorithm for the cover filter minimization problem. Unlike prior work (based on graph coloring) we consider a type of clique-cover problem, involving a new conditional constraint, from which we can find more general relations. In addition to solving the more general problem, the algorithm also corrects flaws present in all prior filter reduction methods. In employing SAT, the algorithm provides a promising basis for future practical development.

中文翻译：

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覆盖组合滤波器及其最小化问题（扩展版）

最近的研究检查了最小化机器人资源足迹的算法。已经研究了一类组合滤波器（广泛使用的概率估计器的离散变体）并介绍了减少其空间需求的方法。本文通过引入我们称为覆盖组合过滤器的自然泛化来扩展现有的组合过滤器。在解决新的——但仍然是 NP 完全的——覆盖过滤器最小化问题时，这篇论文表明，以前认为关于组合过滤器的多个概念（实际上是推测、声称或假设）实际上是错误的. 例如，最小化不会产生等价关系。我们给出了覆盖滤波器最小化问题的精确算法。与之前的工作（基于图着色）不同，我们考虑一种类型的集团覆盖问题，涉及一个新的条件约束，从中我们可以找到更一般的关系。除了解决更一般的问题外，该算法还纠正了所有先前过滤器缩减方法中存在的缺陷。在使用 SAT 时，该算法为未来的实际开发提供了有希望的基础。