Algorithms which learn environments represented by automata in the past have had complexity scaling with the number of states in the automaton, which can be exponentially large even for automata recognizing regular expressions with a small description length. We thus formalize a compositional language that can construct automata as transformations between certain types of category, representable as string diagrams, which better reflects the description complexity of various automata. We define complexity constraints on this framework by having them operate on categories enriched over filtered sets, and using these constraints, we prove elementary results on the runtime and expressivity of a subset of these transformations which operate deterministically on finite state spaces. These string diagrams, or "string machines," are themselves morphisms in a category, so it is possible for string machines to create other string machines in runtime to model computations which take more than constant memory. We prove sufficient conditions for polynomial runtime guarantees on these, which can help develop complexity constraints on string machines which also encapsulate runtime complexity.

翻译：过去，学习由自动机表示的环境的算法，其复杂度与自动机的状态数成比例，而即使对于识别具有小描述长度的正则表达式的自动机，状态数也可能呈指数级增长。因此，我们形式化了一种组合语言，该语言可以将自动机构建为特定类型范畴之间的变换，并以字符串图表示，从而更好地反映各种自动机的描述复杂度。我们通过让这些变换在过滤集富化范畴上运作，并利用这些约束来定义此框架上的复杂度限制，进而证明了在有限状态空间上确定性运作的变换子集的运行时和表达性的基本结果。这些字符串图，或称“字符串机”，本身也是某个范畴中的态射，因此字符串机有可能在运行时创建其他字符串机，以模拟需要超过恒定内存的计算。我们证明了这些机器具有多项式运行时保证的充分条件，这有助于同时封装运行时复杂度的字符串机复杂度约束的建立。