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：机器人必须保留最少多少信息才能完成其任务？为设计经济型机器人，现有关于组合滤波器缩减的文献通过算法方法探讨了这一问题。由于无损状态压缩是NP难问题，先前研究除了提出最小化算法外，还考察了多种具备特定性质从而能高效求解的特例。作为对这些发现的补充，本文从参数化复杂性的视角深化了当前理解。通过将问题转化为最小团覆盖，我们提出了一个针对一般缩减问题的固定参数易解算法。该转化引入了由输入滤波器中顺序依赖关系编码的新约束——部分约束可修复，其余通过枚举处理。通过该方法，我们识别了基于约束间耦合性（以高度和宽度概念表示）的影响滤波器缩减的参数，这些参数补充了无约束最小团覆盖问题中已有的结构参数。