This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system for the internal system which is a transition system over a space of information states that reflect a robot's or other observer's perspective based on limited sensing, memory, computation, and actuation. An information transition system is viewed as a filter and a policy or plan is viewed as a function that labels the states of this information transition system. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.

翻译：本文在动作与观测历史框架下，探讨内部系统（机器人算法或软件）与外部系统（机器人本体及其环境）交互过程中信息编码与处理的下界。两者均被建模为迁移系统。我们旨在确定足以完成被动（过滤）与主动（规划）任务的最弱内部系统。为此引入内部系统的信息迁移系统概念，该迁移系统建立在信息状态空间之上，通过有限感知、存储、计算与执行能力反映机器人或其他观测者的视角。信息迁移系统被视作滤波器，而策略或规划则被定义为标注该信息迁移系统各状态的函数。无论内部系统是通过学习算法、规划算法还是人类洞察力获得，我们均需探明给定机器人硬件与任务下的可行性极限。在一般性框架下，我们证明在合理的等价假设条件下最小信息迁移系统存在，并在某些普适条件下具有唯一性。进而将该理论应用于多个问题以产生新见解，包括最优传感器融合/滤波、基本规划任务求解，以及基于输入-输出关系建模系统的最小表示发现。