What is the minimal information that a robot must retain to achieve its task? To design economical robots, the literature dealing with reduction of combinatorial filters approaches this problem algorithmically.As lossless state compression is NP-hard, prior work has examined, along with minimization algorithms, a variety of special cases in which specific properties enable efficient solution. Complementing those findings, this paper refines the present understanding from the perspective of parameterized complexity. We give a fixed-parameter tractable algorithm for the general reduction problem by exploiting a transformation into minimal clique covering. The transformation introduces new constraints that arise from sequential dependencies encoded within the input filter -- some of these constraints can be repaired, others are treated through enumeration. Through this approach, we identify parameters affecting filter reduction that are based upon inter-constraint couplings (expressed as a notion of their height and width), which add to the structural parameters present in the unconstrained problem of minimal clique covering.

翻译：机器为完成任务必须保留的最小信息量是多少？为设计经济型机器人，现有关于组合滤波器约简的文献采用算法方法探讨此问题。由于无损状态压缩是NP难题，先前研究除最小化算法外，还考察了多种特殊情形——这些情形中特定性质可实现高效求解。作为这些发现的补充，本文从参数化复杂性的视角深化现有认知。我们通过将一般约简问题转化为最小团覆盖问题，给出一个固定参数可解算法。该转化引入了由输入滤波器中编码的时序依赖关系产生的新约束——部分约束可修复，其余则通过枚举处理。通过此方法，我们识别出影响滤波器约简的参数，这些参数基于约束间耦合关系（以其"高度"与"宽度"表示），它们补充了无约束最小团覆盖问题中存在的结构参数。