基于因式分解系统的极小概念
Minimality Notions via Factorization Systems
摘要：
对于基于状态的系统的最小化（即减少状态的数量，同时保留系统的语义），有两个明显的方面：删除系统中不必要的状态和合并系统中的冗余状态。本文通过定义一个抽象的极小性概念，将余代数的这两个方面联系起来。抽象概念极小性和极小化存在于具有因子分解系统的一般范畴中。我们将找到确保最小化方面的唯一性、存在性和函性的范畴标准。这些结果的证明实例那些可达性和可观测性最小化在标准的余代数文献。最后，我们将看到最小化的两个方面如何相互作用，以及在什么标准下它们可以以任何顺序排序，就像自动机最小化一样。
英文摘要：
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 aspects on coalgebras by defining an abstract notion of minimality. The abstract notion 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.
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