论文标题
通过分解系统和示例的最小概念
Minimality Notions via Factorization Systems and Examples
论文作者
论文摘要
为了最大程度地减少状态系统（即在保留系统语义的同时减少状态数量），有两个明显的方面：删除系统的不必要状态并合并系统中的冗余状态。在本文中，我们通过定义最小的抽象概念来将有关山地的两个最小化方面联系起来。 抽象的概念最小化和最小化具有分解系统的一般类别。我们将在类别上找到确保最小化方面的独特性，存在和功能性的标准。这些结果的证据实例化了标准煤炭文献中的可及性和可观察性最小化。最后，我们将看到最小化的两个方面如何相互作用，并且在哪些标准下可以按任何顺序进行测序，例如在自动机最小化中。
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two minimization aspects on coalgebras by defining an abstract notion of minimality. The abstract notions minimality and minimization live in a general category with a factorization system. We will find criteria on the category that ensure uniqueness, existence, and functoriality of the minimization aspects. The proofs of these results instantiate to those for reachability and observability minimization in the standard coalgebra literature. Finally, we will see how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization.
